Question

(4x−2) 2 +(3x+1) 2 =25x 2 −3

Answer 1

(4x−2)²+(3x+1)²=25х²−3

16х²-16х+4+9х²+6х+1=25х²−3

-10х=-8

х=0.8

Answer 2

To solve the equation (4x−2)² + (3x+1)² = 25x² - 3, we need to expand and simplify both sides of the equation and then solve for x.

Let's start by expanding the left-hand side (LHS) of the equation:

(4x - 2)² + (3x + 1)² = (4x - 2)(4x - 2) + (3x + 1)(3x + 1) = (16x² - 8x - 8x + 4) + (9x² + 3x + 3x + 1) = 16x² - 16x + 4 + 9x² + 6x + 1 = 25x² - 10x + 5

Now, the equation becomes:

25x² - 10x + 5 = 25x² - 3

Next, we want to isolate x on one side of the equation. Let's move all terms with x to one side:

25x² - 25x² - 10x + 5 = 25x² - 25x² - 3

Simplifying further:

-10x + 5 = -3

Now, let's move the constant term to the other side:

-10x = -3 - 5 -10x = -8

Finally, to find the value of x, divide both sides by -10:

x = -8 / -10 x = 0.8

So, the solution to the equation is x = 0.8.