Question

if a2+1/a2=7 the find the value of (a)a+1/a (b) a-1/a (c) A3+1/a3​

Answer 1

Answer:

$a. 3, b.\sqrt{5}, c. 18$

Step-by-step explanation:

$a^2+\frac{1}{a^2}=7\\\\\implies (a+\frac{1}{a})^2-2*a*\frac{1}{a}=7\\\\\implies (a+\frac{1}{a})^2 = 9\\\\\implies (a+\frac{1}{a}) = 3$

Again

$a^2+\frac{1}{a^2}=7\\\\\implies(a-\frac{1}{a})^2+2*a*\frac{1}{a}=7\\\\\implies(a-\frac{1}{a})^2=7-2=5\\\\\implies(a-\frac{1}{a}) = \sqrt{5}$

$a^3+\frac{1}{a^3} = (a+\frac{1}{a})^3-3*a*\frac{1}{a} (a+\frac{1}{a})\\\\\implies 3^3 -3^2 = 18 as (a+\frac{1}{a}) = 3 (proved)$