Question

(х+7)4 -17(х+7)2 +16=0

Answer 1

Ответ: x= -97

/15

Вот так

Answer 2

To solve the quadratic equation (х+7)4 - 17(х+7)2 + 16 = 0, we can make a substitution to simplify the equation. Let's substitute (х+7)2 with another variable, say, a:

Let a = (х+7)2

Now we have the equation a2 - 17a + 16 = 0, which is a quadratic equation in variable a. We can solve this equation by factoring or using the quadratic formula.

Factoring: (a - 1)(a - 16) = 0

Setting each factor equal to zero: a - 1 = 0 or a - 16 = 0

Solving for a in each case: a = 1 or a = 16

Now we substitute back the value of a: (х+7)2 = 1 or (х+7)2 = 16

Taking the square root of both sides: х + 7 = ±1 or х + 7 = ±4

Solving for х in each case: х = -7 + 1 or х = -7 - 1 or х = -7 + 4 or х = -7 - 4

Simplifying: х = -6 or х = -8 or х = -3 or х = -11

Therefore, the solutions to the equation (х+7)4 - 17(х+7)2 + 16 = 0 are х = -6, х = -8, х = -3, and х = -11.