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

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Joined: 13 May 2017
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What is the sum of all values of x that satisfies the equation  [#permalink]

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23 Nov 2018, 03:51
1
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:40) correct 42% (02:11) wrong based on 32 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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Joined: 26 Feb 2016
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Location: India
GPA: 3.12
What is the sum of all values of x that satisfies the equation  [#permalink]

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23 Nov 2018, 05:40
1
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 &nbs [#permalink] 23 Nov 2018, 05:40
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