Question

If one root of $1 + \sqrt{2}$ be square of the other, then the value of $1 \pm \sqrt{2}$is.

• A. $2^{x + 2}27^{x/(x - 1)} = 9$
• B. $1 - \log_{2}3,2$
• C. 0
• D. None of these

Answer 1

Answer: (A)

$2^{x + 2}27^{x/(x - 1)} = 9$

Answer 2

Let $x$be the two roots. Then

$\frac{x^{2} + 14x + 9}{x^{2} + 2x + 3}$ .....(i) and $\frac{x + 2}{2x^{2} + 3x + 6}$ .....(ii)

On cubing both sides of (i)

$\left( \frac{1}{13},\frac{1}{3} \right)$

$\left\lbrack - \frac{1}{13},\frac{1}{3} \right\rbrack$ [By (i) and (ii)]

$\left( - \frac{1}{3},\frac{1}{13} \right)$.