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What is the sum of all values of x that satisfies the equation

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New post 23 Nov 2018, 04:51
1
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (01:49) correct 43% (02:16) wrong based on 34 sessions

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What is the sum of all values of x that satisfies the equation: \(\sqrt{{6x}}\)=\(\sqrt{{5x+3}}\)+1?

A. 20
B. 24
C. 28
D. 32
E. 36
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What is the sum of all values of x that satisfies the equation  [#permalink]

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New post 23 Nov 2018, 06:40
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rencsee wrote:
What is the sum of all values of x that satisfies the equation: \(\sqrt{{6x}}\)=\(\sqrt{{5x+3}}\)+1?

A. 20
B. 24
C. 28
D. 32
E. 36


For a quadratic equation \(ax^2 + bx + c = 0\) the sum of the roots is \(\frac{-b}{a}\) and product of roots is \(\frac{c}{a}\)

Equation can be re-written as \(\sqrt{{6x}}\) - 1 = \(\sqrt{{5x+3}}\)

Squaring on both sides, we get \(6x + 1 - 2\sqrt{6x} = 5x + 3\) -> \(x - 2\sqrt{6x} - 2 = 0\)

Rewriting, we get \(x - 2 = 2\sqrt{6x}\). Squaring the equation, we will get \(x^2 - 4x + 4 = 4*6x\)

Therefore, the quadratic equation is \(x^2 - 28x + 4 = 0\) and the sum of all the values of x is 28(Option C)
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What is the sum of all values of x that satisfies the equation   [#permalink] 23 Nov 2018, 06:40
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