If a + b = 5 and a2 + b2 = 13, find ab.
If x + \( \dfrac{1}{x}\) = 5, evaluate
(i) x2 + \( \dfrac{1}{x^2}\)
(ii) x4 + \( \dfrac{1}{x^4}\)
Prove that (2a + 3b)2 + (2a – 3b)2 = 8a2 + 18b2
Prove that (a + b)2 – (a – b)2 + 4ab
Using suitable identities, evaluate 105 × 107