i कि रा >> (2 Heo ' - ﬂ_ o का 7हर + (cFd) =0 रो

1.	i कि रा >> (2 Heo ' - ﬂ_ o का 7हर + (cFd) =0 रो 25o
Answer» Given that roots of equation(a^2 + b^2)x^2 - 2(ac + bd)x + (c^2 + d^2) = 0 are equal. Then,4(ac+bd)^2 - 4(a^2 + b^2)(c^2 + d^2) = 0 a^2c^2 + b^2d^2 + 2abcd= a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2 2 abcd = a^2d^2 + b^2c^2 a^2d^2 + b^2c^2 - 2abcd = 0 (ad - bc)^2 = 0 ad = bc a/b = c/d Hence proved

i कि रा >> (2 Heo ' - ﬂ_ o का 7हर + (cFd) =0 रो 25o

Answer»

Given that roots of equation(a^2 + b^2)x^2 - 2(ac + bd)x + (c^2 + d^2) = 0 are equal.

Then,4(ac+bd)^2 - 4(a^2 + b^2)(c^2 + d^2) = 0

a^2c^2 + b^2d^2 + 2abcd= a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2

2 abcd = a^2d^2 + b^2c^2

a^2d^2 + b^2c^2 - 2abcd = 0

(ad - bc)^2 = 0

ad = bc

a/b = c/d

Hence proved