KNGD785
08.12.2019 •
Mathematics
If alpha and beta are the zeroes of quadratic polynomial ax^2+bx+c , then find alpha^4+beta^4
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Ответ:
AB = c/a and A + B = -b/a
A^4 + B^4 = (A^2 + B^2)^2 - 2A^2B^2
= [(A + B)^2 - 2AB] ^2 - 2A^2B^2
Plugging in the values for A+B and AB we get
A^4 + B^4 = [(-b/a)^2 - 2c/a]^2 - 2(c/a)^2
= (b^2 / a^2 - 2c / a)^2 - 2c^2/a^2
= (b^2 - 2ac)^2 - 2c^2
a^4 a^2
= (b^2 - 2ac)^2 - 2a^2c^2
a^4
Ответ:
Lenght: 26.08 mm
Area: 782.36 mm^2
Step-by-step explanation: