If $(a + b) = 10$ and $a b = 20$ , find $a^{2} + b^{2}$ and $(a - b)^{2}$

Open in App

Solution

(i) $a^{2} + b^{2} = (a + b)^{2} - 2 a b$ [Substituting $a + b = 10, a b = 20]$
$a^{2} + b^{2} = (10)^{2} - 2 (20)$
$= 100 - 40 = 60$
$a^{2} + b^{2} = 60$
(ii) $(a - b)^{2} = (a + b)^{2} - 4 a b$ [Substituting $a + b = 10, a b = 20]$
$= (10)^{2} - 4 (20)$
$= 100 - 80$
$(a - b)^{2} = 20$

Suggest Corrections

Similar questions

a + b = 10, a b = 32

a^{2} + b^{2}, a - b

a^{2} - b^{2}

a + b = 10, a b = 24

a^{2} + b^{2}

If a + b = 10 and ab = 16, find the value of $a^{2} - a b + b^{2} a n d a^{2} + a b + b^{2}$ .

a^{2} + b^{2} + c^{2} = 20

a + b + c = 0

a b + b c + c a + 10

Join BYJU'S Learning Program