jika a dan b adalah akar akar 11x^2-4x-2 = 0 hitunglah Nilai Dari (1+a+a^2+.....)(1+b+b^2+.....)tolong jawab ya

11x^2 - 4x - 2 = 0
p = 11
q = -4
r = -2

a + b = -q/p = 4/11
ab = r/p = -2/11

deret geometri tak hingga.

(1 + a + a^2 + ... )(1 + b + b^2 + ... ) = (1/(1 - a))(1/(1 - b))
= 1/((1 - a)(1 - b))
= 1/(1 - a - b + ab)
= 1/(1 - (a + b) + ab)
= 1/(1 - 4/11 + (-2/11))
= 1/(1 - 6/11)
= 1/(11/11 - 6/11)
= 1/(5/11)
= 11/5