Question

a²+b² when a+b =9,ab=20​

Answer 1

(i) a2+b2=(a+b)2−2ab [Substituting a+b=10,ab=20]

a2+b2=(10)2−2(20)

=100−40=60

a2+b2=60

(ii) (a−b)2=(a+b)2−4ab[Substituting a+b=10,ab=20]

=(10)2−4(20)

=100−80

(a−b)2=20

Answer 2

$(a + b {)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {9}^{2} = {a}^{2} + {b}^{2} + 2 \times 20 \\ \\ 81 = {a}^{2} + {b }^{2} + 40 \\ \\ 41 = a {}^{2} + {b}^{2}$