If x>0 and √5x=√3x+1, what is the value of 4x^2?
A. 1/2
B. 1
C. 4x-1
D. 10x-1
E. 16x-1
The OA is E.
I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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If x>0 and √5x=√3x+1, what is the value of 4x^2?
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For the sake of clarify, I've added the parentheses to the given equation:
(a - b)² = a² + b² - 2ab.
√(5x) = √(3x) + 1.
Square both sides:
√(5x)² = ((√3x) + 1)²
Simplify the left side and expand the right side:
5x = 3x + 1 + (2)(√(3x))(1)
On the right side, isolate the term with the root:
2x - 1 = 2(√(3x))
Square both sides:
(2x - 1)² = [2(√(3x))]²
Expand the left side and simplify the right side:
4x² + 1 - (2)(2x)(1) = (4)(3x)
Simplify:
4x² + 1 - 4x = 12x
Isolate 4x²:
4x² = 16x - 1.
The correct answer is E.
(a + b)² = a² + b² + 2ab.LUANDATO wrote:If x>0 and √(5x) = √(3x) + 1, what is the value of 4x²?
A. 1/2
B. 1
C. 4x-1
D. 10x-1
E. 16x-1
(a - b)² = a² + b² - 2ab.
√(5x) = √(3x) + 1.
Square both sides:
√(5x)² = ((√3x) + 1)²
Simplify the left side and expand the right side:
5x = 3x + 1 + (2)(√(3x))(1)
On the right side, isolate the term with the root:
2x - 1 = 2(√(3x))
Square both sides:
(2x - 1)² = [2(√(3x))]²
Expand the left side and simplify the right side:
4x² + 1 - (2)(2x)(1) = (4)(3x)
Simplify:
4x² + 1 - 4x = 12x
Isolate 4x²:
4x² = 16x - 1.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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