=2 Formual Used: a3+b3=(a+b)(a2+b2−ab) Calculation: We have a+b=2⋯−(i) And
1
a
+
1
b
=2 ⇒a+b=2ab ⇒2=2ab[ from (i) ] ⇒ab=1⋯ (ii) Squaring the equation (i), we get a2+b2+2ab=4 ⇒a2+b2+2×1=4 ⇒a2+b2=2 According to the formula used a3+b3=(a+b)(a2+b2−ab) And from equation (i), (ii) and (iii), we get ⇒a3+b3=2(2−1) ⇒a3+b3=2 ∴ The required value of a3+b3 is 2 .