If a + b = 5, a - b = 1 then let's show that. `8ab (a^2 + b^2)` = 624

Using formula, let's solve each of the following problems- If a^2 + b^2 = 5ab , let's show that frac(a^2)(b^2) + frac(b^2)(a^2) = 23

If |a| lt 1, |b| lt 1 , then show that a(a+b) + a^(2) (a^(2) + b^(2)) + a^(3)(a^(3) + b^(3)) +… = (a^(2))/(1-a^(2)) + (ab)/(1- ab)

Using formula let's show that. (a+2b)^2 + (a-2b)^2 = 2(a^2 + 4b^2)

Using formula let's show that. (3a-4b)^2 + 24ab = 9a^2 +16b^2

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5} . Find A′, B′ , A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′ ∩ B′ .

If sin A+ tan A= a and cos A+ cot A= b, then show that (1+a)^(-2)+(1+b)^(-2)=(1-ab)^(-2)

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7 } . Find A ∩ B and hence show that A ∩ B = B .

If a, b, c are in geometric progression, then show that, (a^(2) + ab + b^(2))/(ab + bc + ca) = (a + b)/(b + c)

if g(x)=(x-a)/x+x/(x-b) then show that g((a+b)/2)=(4ab)/(a^2-b^2)