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# What is the value of x[square_root] 3[/square_root]

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What is the value of x[square_root] 3[/square_root]  [#permalink]

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28 Mar 2019, 22:19
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00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:33) correct 37% (01:47) wrong based on 49 sessions

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What is the value of $$( x\sqrt{3} + y\sqrt{3} ) ^2$$ ?

1. $$2x + 2y = 20$$

2. $$x^2 + xy = 100 - y^2 - xy$$

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Re: What is the value of x[square_root] 3[/square_root]  [#permalink]

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31 Mar 2019, 11:48
AkshdeepS wrote:
What is the value of $$( x\sqrt{3} + y\sqrt{3} ) ^2$$ ?

1. $$2x + 2y = 20$$

2. $$x^2 + xy = 100 - y^2 - xy$$

Statement 1:
Simplify the equation -> x+y=10. Now we should rewrite the expression of the question stem to $$(\sqrt{3}(x+y))^2 = 3(x+y)^2$$.
Now just plug in the x+y=10 -> 300.

Statement 2:
Solving the expression of the question stem using the binomial theorem we get: $$3x^2 + 6xy +3y^2$$.
Next we move the $$y^2$$ and $$-xy$$ from the right side of the S2 equation to the left. Then multiply the whole equation by 3 to get the above equation -> $$3*100 = 300$$

Hence, statement D is correct.
Re: What is the value of x[square_root] 3[/square_root]   [#permalink] 31 Mar 2019, 11:48
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