Question

if the vaue of x=4+root15 then find the value x-1/x​

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

$x = 4 + \sqrt{15} \\ \\ \frac{1}{x} = \frac{1}{4 + \sqrt{15} } \\ = > \frac{1}{x} = \frac{4 - \sqrt{15} }{(4 + \sqrt{15} )(4 - \sqrt{15} )} \\ = > \frac{1}{x} = \frac{4 - \sqrt{15} }{16 - 15} \\ = > \frac{1}{x} = 4 - \sqrt{15} \\ \\ therefore....... \\ \\ x - \frac{1}{x} = 4 + \sqrt{15} - 4 + \sqrt{15} \\ = > x - \frac{1}{x} = 2 \sqrt{15}$

Answer 2

x-1/x

when x= 4+√15

4+√15-1/4+√15

LCM=4+√15

4+√15 × 4+√15-1/4+√15

by applying the first algebraic identity: (a+b)^2=(a+b)(a+b)=a^2+b^2+2ab

therefore, (4)^2 + (√15)^2+2(4)(√15)= 16+15 + 8√15 =31+8√15

so, 31+8√15-1/4+√15 =>30+8√15/4+√15

rationalizing the denominator

30+8√15/4+√15 × 4-√15/4-√15

=> 120-30√15+32√15-1800/16-15

=>2√15-1680/1=2√15-1680

therefore the value of x-1/x = 2√15-1680

hope this helps