Question

Descumpune in factori:

$x^{2} -5x-6$

${2} (5x-7)^{2} -49 x^{2}$

Answer 1

x²-5x-6= x²-6x+x-6=x(x-6)+(x-6)=(x-6)(x+1)

varianta fara 2 din fata
(5x-7)²-49x²=(5x-7-7x)(5x-7+7x)=(-2x-7)(12x-7)

varianta cu 2 in fata
2(5x-7)²-49x²=2(25x²-70x+49)-49x² =50x²-140x+98-49x²=
=x²-140x+98=(x-70+49√2)(x-70-49√2)
Δ=140²-4*98=19600-392=19208=
x₁₂=(140+√19208)/2=70+49√2
x₂=(140-√19208)/2=70-49√2