roots of [x² - 2(a - 1)x - (b + 2)² = 0] are equal. a⁹⁹⁹ + b³ =?
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2016-02-11 11:10 am
✔ 最佳答案
The equation x² - 2(a - 1)x - (b + 2)² = 0 has equal roots.Discriminant, Δ = 0
[-2(a - 1)]² - 4[-(b + 2)]² = 0
4(a - 1)² + 4(b + 2)² = 0
(a - 1)² + (b + 2)² = 0
Since (a - 1)² ≥ 0 and (b + 2)² ≥ 0,
(a - 1)² = 0 and (b + 2)² = 0
a - 1 = 0 and b + 2 = 0
a = 1 and b = -2
a⁹⁹⁹ + b³
= 1⁹⁹⁹ + (-2)³
= 1 - 8
= -7
2016-02-11 1:34 pm
If roots of x^2 -2(a-1)x - (b+2)^2 =0 are equal, then the discriminant 4(a-1)^2
+ 4(b+2)^2 = 0, ie., (a-1)^2 + (b+2)^2 = 0, ie., (a,b) = (1,-2) & a^999 + b^3 =
1^999 + (-2)^3 = 1 -8 = -7.
+ 4(b+2)^2 = 0, ie., (a-1)^2 + (b+2)^2 = 0, ie., (a,b) = (1,-2) & a^999 + b^3 =
1^999 + (-2)^3 = 1 -8 = -7.
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