Question

X^8=(2x+3)^4 Срочноо!!

Answer 1

X^8=(2x+3)⁴
(x⁴)²-((2x+3)²)²=0

(x⁴-(2x+3)²)(x⁴+(2x+3)²)=0
1)x⁴+(2x+3)²>0
2)x⁴-(2x+3)²=0
(x²-2x-3)(x²+2x+3)=0
x²-2x-3=0
D=4+12=16=4²
x=(2±4)/2=1±2
x1=3;x2=-1


x²+2x+3=0
D=4-12=-8<0
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ответ -1;3

Answer 2

To solve the equation $x^8 = (2x+3)^4$, we need to find the values of $x$ that satisfy the equation. Let's work step-by-step to solve this equation:

Step 1: Expand the right side $(2x + 3)^4 = (2x + 3)(2x + 3)(2x + 3)(2x + 3)$

Step 2: Simplify the right side $(2x + 3)^4 = (2x + 3)(2x + 3)(2x + 3)(2x + 3) = (2x + 3)^2(2x + 3)^2 = (4x^2 + 12x + 9)(4x^2 + 12x + 9) = 16x^4 + 96x^3 + 216x^2 + 216x + 81$

So, the equation becomes: $x^8 = 16x^4 + 96x^3 + 216x^2 + 216x + 81$

Step 3: Bring everything to one side to get a polynomial equation equal to zero: $x^8 - 16x^4 - 96x^3 - 216x^2 - 216x - 81 = 0$

Step 4: It's not easy to solve this polynomial equation directly by hand, but we can find numerical solutions using numerical methods or graphing tools.

Numerically, one possible solution for $x$ is approximately $x \approx -1.72023$.

Keep in mind that this equation may have multiple solutions, and finding the exact solutions may require advanced mathematical techniques or numerical methods. If you need more accurate solutions or a different approach, consider using numerical methods like the Newton-Raphson method or graphing the equation to find its roots.