Question

(8x+7)^2(4x+3)(x+1)=9/2

Answer 1

64(x+7/8)^2*(4x^2+7x+3)=9/2

128(x+7/8)^2*(4(x+7/8)^2-49/16+3)-9=0

128(x+7/8)^2*(4(x+7/8)^2-1/16)-9=0   x+7/8=y

128*4y^2-128y/16-9=0  | :2

256y^2-4y-9/2=0  D=16+18*256=68*68

y=(4±68)/512=9/64 и -8

x= (-8*8-7)/8= -71/8

x=(9-7*8)/64= -47/64

Вроде всё правильно.

Answer 2

To solve the equation $(8x+7)^2(4x+3)(x+1) = \frac{9}{2}$, follow these steps:

Step 1: Expand the expressions First, expand the expressions on both sides of the equation. For the left side, expand $(8x+7)^2$, and for the right side, convert $\frac{9}{2}$ into an equivalent expression.

Left side: $(8x+7)^2 = (8x+7)(8x+7) = 64x^2 + 112x + 49$

Right side: $\frac{9}{2} = \frac{9}{2} \cdot 1 = \frac{9}{2} \cdot \frac{2}{2} = \frac{9}{4}$

Now the equation becomes: $64x^2 + 112x + 49)(4x+3)(x+1) = \frac{9}{4}$

Step 2: Multiply both sides by 4 to eliminate the fraction on the right side: $4(64x^2 + 112x + 49)(4x+3)(x+1) = 9$

Step 3: Simplify the equation: $256x^2 + 448x + 196)(4x+3)(x+1) = 9$

Step 4: Subtract 9 from both sides to move all terms to one side of the equation: $256x^2 + 448x + 196)(4x+3)(x+1) - 9 = 0$

Step 5: Solve for x This is a polynomial equation, and it may not have simple analytical solutions. You can attempt to solve it numerically using software or calculators. Alternatively, you can try factoring, but it might be a bit complicated due to the high-degree terms involved.

One approach for solving such equations is to use numerical methods like the Newton-Raphson method or a graphing calculator to approximate the solutions. If you need specific solutions for this equation, you can use appropriate software or calculators to find the numerical solutions.