Question

Equation X square + bx + c is equal to zero is equal to the sum of the cubes of their reciprocals then prove that a b square is equal to 3 square C plus c cube

Answer 1

Given,

let the roots be p and q

p+q = -b/a

pq = c/a

but given,

=>p+q = 1/p² + 1/q²

=>-b/a = p²+q²/p²q²

=>-b/a = (p+q)²-2pq/p²q²

=>-b/a = (-b/a)²-2(c/a)/(c/a)²

=>-b/a = b²/a² - 2(c/a)/c²÷a²

=>-b/a (c²/a²) = b²/a² - 2(c/a)

=>-bc²/a³ = b²/a² - 2(c/a)

=>2(c/a) = b²/a² + bc²/a³

=>2(c/a) = ab²+bc²/a³

=>2(c/a) = b(ab+c²)/a³

=>2(c/a)(a³) = ab²+bc²

=>2ca² = ab² + bc²

=>2 = ab² + bc² / ca²

=>2 = ab²/ca² + bc²/ca²

=>2 = b²/ac + bc/a²

HOPE U UNDERSTAND

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