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28 Jun 2019, 15:00
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The function {x} is defined as the area of a square with diagonal of length x. If x > 0 and {x²} = x², what is the value of x?
A) 1
B) √2
C) √3
D) 2
E) 4
A) 1
B) √2
C) √3
D) 2
E) 4
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utkarshg97
Joined: 26 Jun 2019
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28 Jun 2019, 15:22
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The function {x} is defined as the area of a square with diagonal of length x. If x > 0 and {x²} = x², what is the value of x?
A) 1
B) √2
C) √3
D) 2
E) 4
A) 1
B) √2
C) √3
D) 2
E) 4
=> {x} is f(x) = \([x/\sqrt{2}]^2\)
Now substituting the expansion into the question.
\([x/\sqrt{2}]^4 = x^2\)
=> \((x^4)/4 = x^2\)
\(=> x^2 = 2 \\
=> x = \sqrt{2}\)
___________________________________________________
Please give kudos if you liked the answer.
28 Aug 2019, 06:03
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utkarshg97
=> {x} is f(x) = \([x/\sqrt{2}]^2\)
Now substituting the expansion into the question.
\([x/\sqrt{2}]^4 = x^2\)
=> \((x^4)/4 = x^2\)
\(=> x^2 = 2\\
=> x = \sqrt{2}\)
___________________________________________________
Please give kudos if you liked the answer.
Now substituting the expansion into the question.
\([x/\sqrt{2}]^4 = x^2\)
=> \((x^4)/4 = x^2\)
\(=> x^2 = 2\\
=> x = \sqrt{2}\)
___________________________________________________
Please give kudos if you liked the answer.
utkarshg97, I think there is a small calculation error in your explanation; try substituting "x" by \(\sqrt{2}\) and you will see that both sides of the equation are unequal.
Thus, isn't 2 (Option D) the answer?
\([x/\sqrt{2}]^4 = x^2\)
=> \((x^4)/4 = x^2\)
=> \((x^4)/(x^2) = 4\)
=> \(x^2 = 4\)
=> \(x = 2\) (since x>0)
Please advise if you reckon I am wrong.
