Question

(5х-1)*(х+2)+3(х-4)*(х+4)=2(2х+3)^-8

Answer 1

5x2+10x-x-2+3x2-48=8x2+24x+18-8
-15x=60
x= -4

Answer 2

To solve the equation (5x-1)(x+2) + 3(x-4)(x+4) = 2(2x+3)^-8, we'll start by simplifying both sides of the equation step by step.

Step 1: Expand the expressions on both sides. On the left side: (5x-1)(x+2) + 3(x-4)(x+4) = (5x^2 + 9x - 2) + (3x^2 - 9x - 48)

On the right side: 2(2x+3)^-8 = 2/(2x+3)^8

Step 2: Combine like terms on the left side: (5x^2 + 9x - 2) + (3x^2 - 9x - 48) = 8x^2 - 48

Now, the equation becomes: 8x^2 - 48 = 2/(2x+3)^8

Step 3: Move all the terms to one side to set the equation equal to zero: 8x^2 - 48 - 2/(2x+3)^8 = 0

Step 4: Now, we can solve this equation. However, it is worth mentioning that this equation is a polynomial of degree 8 due to the (2x+3)^8 term, and solving it analytically may be quite complex. We can use numerical methods or graphing techniques to approximate the solutions.

One way to approach this is to graph the function y = 8x^2 - 48 - 2/(2x+3)^8 and find the x-values where the graph intersects the x-axis (where y = 0). You can use graphing calculators or software like Desmos or Wolfram Alpha to graph the equation and find the approximate solutions.

Keep in mind that there may be multiple solutions to this equation, and the exact values will depend on the precision of the numerical methods used.