Navjyot Kalra
Last Activity: 10 Years ago
Sol. Let α, β be the roots of eq. ax2 + bx + c = 0
According to the question,
Β = αn
Also α + β = -b/a ; αβ = c/a
α β = c/a ⇒ α. α n = c/a ⇒ α = (c/a)1/n + 1
then α + β = - b/a ⇒ α + αn = -b/a
or (c/a)1/n + 1 + (c/a)n/n + 1 = -b/a
⇒ a .(c/a)1/n + 1 + a .(c/a)n/n + 1 + b = 0
⇒ an/n + 1 c1/n + 1 + a1/n + 1 c n/n + 1 + b = 0
⇒ (an c) 1/n + 1 + (can) 1/n + 1 + b = 0
Hence proved.
