Question

X+1/x=a and x-1/x=b then a2-b2

Answer 1

Answer:

$\huge\bold\red{ANSWER}$

Step-by-step explanation:

$\large{\underline{\rm{\red{SOLUTION :}}}}$

$\implies \sf x+\frac{1}{x}=a\\ \\ \sf S.O.B.S\\ \\ \sf x^2+\frac{1}{x^2}+2=a^2\:\:\:(1)\\ \\ \implies \sf x-\frac{1}{x}=b\\ \\ \sf S.O.B.S\\ \\ x^2+\frac{1}{x^2}-2=b^2\:\:(2)\\ \\ \implies \sf from\:1\:and\:2\:we\:get\\ \\ \implies \sf a^2-b^2=x^2+\frac{1}{x^2}+2-(x^2+\frac{1}{x^2}-2)\\ \\ \implies \sf a^2-b^2=x^2+\frac{1}{x^2}+2-x^2-\frac{1}{x^2}+2\\ \\ \implies \sf a^2-b^2=4$