Question

If a + b = √5 and ab = √3, then the value of (a2 + b2)
(a) 5 (b) 4 (c) 2 (d) 1​

Answer 1

Step-by-step explanation:

Given :

$a + b = \sqrt{5 \:} \: and \: ab = \sqrt{3}$

we know that

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

let this be equation 1

We are asked to find :

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

therefore substituting the given values in equation 1 we get

${ (\sqrt{5}) }^{2} = {a}^{2} + {b}^{2} + 2 \times \sqrt{3}$

$5 - 2 \sqrt{3} = {a}^{2} + {b}^{2}$

this is the correct answer