If $a + b = 5$ and $a - b = 4$ , find $a^{2} + b^{2}$ and $a b$

Open in App

Solution

using,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$
$(a - b)^{2} = a^{2} + b^{2} - 2 a b$
adding two eqs $a^{2} + b^{2} = \frac{(a + b)^{2} + (a - b)^{2}}{2} = \frac{5^{2} + 4^{2}}{2} = 20.5$
substracting the two values $a b = \frac{(a + b)^{-} (a - b)^{2}}{4} = 2.25$

Suggest Corrections

Similar questions

a^{2} + b^{2}

a + b = 5

a b = 6

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} = 13

Join BYJU'S Learning Program