What is the value of x in the equation \sqrt{1+x}/x-\sqrtx/{1+x}=1/\sqrt6?

RRB Junior Engineer Stage 1 Model Papers 5

Question : 8 of 100

Marks: +1, -0

What is the value of x in the equation

√{1+x}/x-√x/{1+x}=1/√6

Solution:

√{1+x}/x-√x/{1+x}=1/√6

By squaring both sides

(√{1+x}/x-√x/{1+x})=(1/6)^2

⇒{1+x}/x+{x}/{1+x}+x-2.{1+x}/x.√x/{1+x}=1/√6

⇒{(1+x)+x^2}/{x(1+x)}=13/6

⇒{1+x^2+2+x^2}/{x+x^2}=13/6

{2x^2+2x+1}/{x^2+x}=13/6

⇒ 13x^2+ 13x =12x^2+ 12x + 6

⇒ x^2+ 3x – 2x – 6 = 0

⇒ x (x + 3) – 2 (x + 3) = 0

⇒ (x – 2) (x + 3) = 0

⇒ x – 2 = 0 ∴ x = 2

⇒ x + 3 = 0 ∴ x = – 3

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