Question

please answer the 1st question with explanation.. ​

Answer 1

$\mathsf{Given :\;\big[a^2 + b^2\big]^3 = \big[a^3 + b^3\big]^2}$

★  We know that : (P + Q)³ = P³ + Q³ + 3PQ(P + Q)

★  We know that : (P + Q)² = P² + Q² + 2PQ

$\mathsf{\implies \big[a^2\big]^3 + \big[b^2\big]^3 + 3a^2b^2\big[a^2 + b^2\big] = \big[a^3\big]^2 + \big[b^3\big]^2 + 2a^3b^3}$

$\mathsf{\implies \big[a]^6 + \big[b\big]^6 + 3(ab)^2\big[a^2 + b^2\big] = \big[a\big]^6 + \big[b\big]^6 + 2(ab)^3}$

$\mathsf{\implies 3(ab)^2\big[a^2 + b^2\big] = 2(ab)^3}$

$\mathsf{\implies a^2 + b^2 = \dfrac{2(ab)^3}{3(ab)^2}}$

$\mathsf{\implies a^2 + b^2 = \dfrac{2ab}{3}}$

$\mathsf{Now,\;Consider : \dfrac{a}{b} + \dfrac{b}{a}}$

$\mathsf{\implies \dfrac{a^2 + b^2}{ab}}$

Substituting the value of (a² + b²) in above expression, We get :

$\mathsf{\implies \dfrac{\dfrac{2ab}{3}}{ab}}$

$\mathsf{\implies \dfrac{2ab}{3ab}}}$

$\mathsf{\implies \dfrac{2}{3}}}$

Answer 2

This is kinda difficult question we have to figure out what is the number of ‘a/b plus b/a’, so our aim is to find out the number of this, we use a math formula to calculate and use the condition ‘ab is not 0’ by dividing with ab. That’s the point