3x²-2x+6+2x²-3x+6=5x²-5x+12
3x²-2x+6-2x²+3x-6=x²+x
(3x²-2x+6)(2x²-3x+6)=6x^4-9x³+18x²-4x³+6x²-12x+12x²-18x+36=6x^4-13x³+36x²-30x+36
Решение
<span>4(4x−23)^2−19(4x−23)+12=0
</span>4x - 23 = z
4z² - 19z + 12 = 0
D = 361 - 4*4*12 = 169
z₁ = (19 - 13)/8
z₁ = 0,75
z₂ = (19 + 13)/8
z₂ = 32/8
z₂ = 4
4x - 23 = 0,75
4x = 0,75 + 23
x₁ = 23,75/4
x₁ = 5,9375
4x - 23 = 4
4x = 4 + 23
4x = 27
x₂ = 6,75
Ответ: x₁ = 5,9375 ; x₂ = 6,75
пусть натуральное число это x
тогда
(x+1)^2-x^2=65
x^2+2x+1-x^2=65
2x+1=65
2x=64
x=32