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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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New post 28 Mar 2019, 22:19
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:33) correct 38% (01:47) wrong based on 48 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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New post 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.
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Re: What is the value of x[square_root] 3[/square_root]   [#permalink] 31 Mar 2019, 11:48
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What is the value of x[square_root] 3[/square_root]

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