If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (2024)

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (1)

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Bunuel

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]07 Apr 2019, 21:30

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (15)

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tìm số tự nhiên x,y :biết x+y/x^2+y^2=7/25

If \(x + y = 7\) and \(x^2 + y^2 = 25\), then which one of the following equals the value of \(x^3 + y^3\) ?

(A) 7

(B) 25

(C) 35

(D) 65

(E) 91

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (22)

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Archit3110

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (23)

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545 Q79 V79 DI73 If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (24)

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Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]08 Apr 2019, 01:16

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Bunuel wrote:

If \(x + y = 7\) and \(x^2 + y^2 = 25\), then which one of the following equals the value of \(x^3 + y^3\) ?

(A) 7

(B) 25

(C) 35

(D) 65

(E) 91

\(x^2 + y^2 = 25\)
solve with x+y=7
we get y=4,3 and x= 3,4
x^3+y^3 = 27+64 ; 91
IMO E

If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (27)

S

thyagi

Manager

If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (28)

Joined: 19 Jan 2019

Posts: 82

GMAT 1: 650 Q49 V30

Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]08 Apr 2019, 07:34

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X^3 + y^3 = (X+y)(x^2+y^2-xy) --(1)

(X+y)^2 = x^2+y^2+2xy
49-25=2xy
2xy = 24
Xy=12

Substitute xy=12.
7(25-12)
7*13 = 91..

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (30)

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lucajava

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (31)

Joined: 21 Feb 2019

Posts: 69

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Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]08 Apr 2019, 07:44

\(x + y = 7\)
\(x^2 + y^2 = 25\)

\(7\) as sum of two numbers is given by: 4+3; 6+1; 5+2 ...

If the second equation is verified, pick them; otherwise, reject them.

\(4^2 + 3^2 = 16\)? Yes. Pick them.

\(4^3 + 3^3 = 64 + 27 = 91\). Correct answer: E.

If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (33)

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BrentGMATPrepNow

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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (34)

Joined: 12 Sep 2015

Posts: 6814

Location: Canada

Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]08 Apr 2019, 09:24

Expert Reply

Top Contributor

Bunuel wrote:

If \(x + y = 7\) and \(x^2 + y^2 = 25\), then which one of the following equals the value of \(x^3 + y^3\) ?

(A) 7

(B) 25

(C) 35

(D) 65

(E) 91

----ASIDE---------------
We COULD use some algebra to solve the question.
First rewrite the first equation as x = 7 - y
Then take second equation and replace x with 7 - y to get: (7 - y)² + y² = 25
When we eventually solve the system, we get two possible solutions:
Solution #1: x = 3 and y = 4
Solution #2: x = 4 and y = 3
-----------------------------

Solving the question is the above way takes time. So, before resorting to algebra, we might first see if we can solve the question through inspection.
If we do so, we might quickly realize that one value must be 3 and the other must be 4.

So, x³ + y³ = 3³ + 4³
= 27 + 64
= 91

Answer: E

Cheers,
Brent

If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (36)

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ScottTargetTestPrep

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Location: United States (CA)

Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]10 Apr 2019, 17:48

Expert Reply

Bunuel wrote:

If \(x + y = 7\) and \(x^2 + y^2 = 25\), then which one of the following equals the value of \(x^3 + y^3\) ?

(A) 7

(B) 25

(C) 35

(D) 65

(E) 91

Since x + y = 7, (x + y)^2 = 7^2 → x^2 + 2xy + y^2 = 49. Since x^2 + y^2 = 25, we have 25 + 2xy = 49 → 2xy = 24 → xy = 12.

Recall that x^3 + y^3 factored as (x + y)(x^2 - xy + y^2), so we have:

x^3 + y^3 = (7)(25 - 12) = 7(13) = 91

Answer: E
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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal (39)

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Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]24 Feb 2024, 05:43

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Re: If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal[#permalink]

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