Question

If a^2 = 5a – 3, b^2 = 5b – 3 then the value of a/b + b/a is-

Answer 1

Question :–

▪︎ If a² = 5a – 3, b² = 5b – 3 then the value of a/b + b/a = ?

ANSWER :–

▪︎a/b + b/a = 19/3

EXPLANATION :–

GIVEN :–

▪︎ Equations are a² = 5a – 3 and b² = 5b – 3.

TO FIND :–

▪︎ a/b + b/a = ?

SOLUTION :–

▪︎ Let's assume a quadratic equation x² = 5x - 3 which have two roots a and b , because roots are always satisfy the polynomial.

▪︎ Hence a quadratic equation x² - 5x + 3 = 0 which have two roots a and b.

▪︎ We know that –

• Sum of roots = a + b = -(-5)/(1) = 5

• Product of roots = a.b = (3)/(1) = 3

▪︎ So that –

= a/b + b/a

= (a² + b²)/(ab)

• Using identity –

⇨ (a + b)² = a² + b² + 2ab

= [(a + b)² - 2ab]/(ab)

• Now put the values –

= [(5)² - 2(3)]/(3)

= (25 - 6)/3

= (19/3)

Hence , (a/b) + (b/a) = 19/3