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Sub 505 (Easy)|   Algebra|      
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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 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 equals the value of \(x^3 + y^3\) ?

(A) 7

(B) 25

(C) 35

(D) 65

(E) 91
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E
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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal 08 Apr 2019, 01:16
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Bunuel
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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\(x^2 + y^2 = 25\)
solve with x+y=7
we get y=4,3 and x= 3,4
x^3+y^3 = 27+64 ; 91
IMO E
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GMAT 1: 650 Q49 V30
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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal 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 08 Apr 2019, 07:44
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\(x + y = 7\)
\(x^2 + y^2 = 25\)

\(7\) 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.
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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal 08 Apr 2019, 09:24
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Bunuel
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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----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
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If x + y = 7 and x^2 + y^2 = 25, then which one of the following equal 10 Apr 2019, 17:48
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Bunuel
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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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 24 Feb 2024, 05:43
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