Its a easy one

Algebra Level 2

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The answer is 9.

Arpit Dhimanj by Arpit Dhimanj , 23, India

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4 solutions

x + 1 − x − 1 = 1 → x + 1 = 1 + x − 1 \color{#D61F06}{\sqrt{x+1}-\sqrt{x-1}=1\rightarrow \sqrt{x+1}=1+\sqrt{x-1}} x + 1 = 1 + 2 x − 1 + x − 1 → 1 = 2 x − 1 \color{#69047E}{x+1=1+2\sqrt{x-1}+x-1\rightarrow 1=2\sqrt{x-1}} 1 = 4 x + 4 → 4 x = 4 + 1 = 5 → x = 5 4 \color{#3D99F6}{1=4x+4\rightarrow 4x=4+1=5\rightarrow x=\frac{5}{4}} So p + q = 5 + 4 = 9 \color{#20A900}{p+q=5+4=\boxed{9}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

In the second last line it should be 1 = 4x - 4

Karanveer Thakur - 5 years, 12 months ago

X=5/4 is the solution

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Multiply both sides by x + 1 + x − 1 \sqrt{x+1}+\sqrt{x-1} (it is positive). We then have x + 1 + x − 1 = 2 \sqrt{x+1}+\sqrt{x-1}=2 . Subtract the equations and you'll see that 2 x − 1 = 1 ⟹ x − 1 = 1 2 \displaystyle 2\sqrt{x-1}=1\implies\sqrt{x-1}=\frac{1}{2} ⟹ x − 1 = 1 4 ⟹ x = 5 4 \displaystyle\implies x-1=\frac{1}{4}\implies \boxed{x=\frac{5}{4}}

mathh mathh - 6 years, 11 months ago
Tina Chatterjee
Jul 29, 2014

take root over(x-1) in the other side...and then square both sides..

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Alex Yu
Jul 17, 2014

Sorry but how is 9 coprime?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

5 and 4 are co-prime

Tanjim Faruk - 6 years, 11 months ago

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