Question

If a=8+3 under root 7 and b = 1/a then find the value of a^2+b^2

Answer 1

ANSWER:

given

$a = 8 + 3 \sqrt{7}$

$b = \dfrac{1}{a}$

REQUIRED TO FIND:

${a}^{2} + {b}^{2}$

METHOD :

answer is in the attachment

as we know the value of a by question

we need to substitute value so we get b

and factorise it

IDENTITIES USED:

$> {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

we can also direct substitute the values instead of using identities.