[Math Revolution GMAT math practice question]
If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?
A. 28
B. 39
C. 50
D. 61
E. 72
If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?
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- Max@Math Revolution
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$$? = {\left( {x + y} \right)^2}$$Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?
A. 28
B. 39
C. 50
D. 61
E. 72
$$\left\{ \matrix{
{x^2} + {y^2} = 28 \hfill \cr
2xy = 2 \cdot 11 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,? = 28 + 2 \cdot 11 = 50$$
This solution follows the notations and rationale taught in the GMATH method.
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Every test-taker should know the following quadratic identities:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?
A. 28
B. 39
C. 50
D. 61
E. 72
(x+y)² = x² + y² + 2xy
(x-y)² = x² + y² - 2xy
(x+y)(x-y)² = x² - y²
Substituting x²+y²=28 and xy=11 into (x+y)² = x² + y² + 2xy, we get:
(x+y)² = 28 + 2*11 = 50.
The correct answer is C.
An alternate approach is to BALLPARK.
x and y must have a product of 11, while x²+y² = 28.
If x=3 and y=4, then xy=12 and x²+y² = 3²+4² = 25.
The values in blue are reasonably close to the values in red.
If x=3 and y=4, then (x+y)² = (3+4)² = 49.
Thus, the correct answer must be close to 49.
Only C is viable.
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- Max@Math Revolution
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=>
(x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 2*11 = 28 + 22 = 50.
Therefore, the answer is C.
Answer: C
(x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 2*11 = 28 + 22 = 50.
Therefore, the answer is C.
Answer: C
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If we expand the expression (x + y)^2, we obtain x^2 + y^2 + 2xy. We can now evaluate the new expression by substituting the given values :Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?
A. 28
B. 39
C. 50
D. 61
E. 72
28 + 2 x 11 = 28 + 22 = 50
Answer: C
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