Question

Va rog muuuult....
F:R->R, f(x)=x^2-7x+8

Calculați:x1^2+x2^2
X1^3+x2^3

Answer 1

Explicație pas cu pas:

f(x)=x^2-7x+8

x₁+x₂=7

x₁*x₂=8

x₁²+x₂²=(x₁+x₂)²-2*x₁*x₂=7²-2*8=49-16=33

x₁³+x₂³=(x₁+x₂)(x₁²-x₁*x₂+x₂²)=7(33-8)=7*25=175

Bafta!

Answer 2

$\mathrm{x^2-7x+8 = 0} \\ \\ \mathrm{x_1^2+x_2^2-7(x_1+x_2)+2\cdot 8 = 0 \Rightarrow x_1^2+x_2^2 = 7(x_1+x_2)-16\Rightarrow}\\\Rightarrow\mathrm{x_1^2+x_2^2 = 7\cdot 7-16 = 33}\\ \\\mathrm{x^3-7x^2+8x = 0} \\\\\mathrm{x_1^3+x_2^3-7(x_1^2+x_2^2)+8(x_1+x_2) = 0 \Rightarrow }\\ \Rightarrow \mathrm{x_1^3+x_3^3 =7(x_1^2+x_2^2)-8(x_1+x_2) = 7\cdot 33 -8\cdot 7 = 175}$