Question

Tenglamani yeching1) 16x² - (4x – 5)² =15;2) 64x2 - (3 – 8x) = 87;​

Answer 1

Ответ:

1) x = 1; 2) x = 2

Объяснение:

$1) \\16x^{2} -(16x^{2} - 40x + 25)=15\\16x^{2}-16x^{2}+40x-25=15\\40x=15+25\\40x=40\\x=1\\2)\\64x^{2}-(9-48x+64x^{2})=87\\64x^{2} -9+48x-64x^{2}=87\\48x=87+9=96\\x=2$

Answer 2

Let's solve the two equations you've provided:

1. $16x^2 - (4x - 5)^2 = 15$:

To solve this equation, we can first expand the square term on the left side and then simplify:

$16x^2 - (4x - 5)^2 = 15$

Expand the square:

$16x^2 - (16x^2 - 40x + 25) = 15$

Now distribute the negative sign to both terms inside the parentheses:

$16x^2 - 16x^2 + 40x - 25 = 15$

Now, simplify the equation:

$40x - 25 = 15$

Add 25 to both sides:

$40x = 15 + 25$

$40x = 40$

Now, divide by 40:

$x = \frac{40}{40}$

$x = 1$

So, the solution to the first equation is $x = 1$.

2. $64x^2 - (3 - 8x) = 87$:

Let's solve this equation:

$64x^2 - (3 - 8x) = 87$

First, distribute the negative sign to both terms inside the parentheses:

$64x^2 - 3 + 8x = 87$

Now, move the constant term (-3) to the other side of the equation by adding 3 to both sides:

$64x^2 + 8x = 87 + 3$

Simplify:

$64x^2 + 8x = 90$

Now, we can divide both sides by 8 to simplify further:

$\frac{64x^2}{8} + \frac{8x}{8} = \frac{90}{8}$

Simplify:

$8x^2 + x = \frac{45}{4}$

Now, we have a quadratic equation. To solve it, we can set it equal to zero:

$8x^2 + x - \frac{45}{4} = 0$

Now, you can solve this quadratic equation using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this equation, $a = 8$, $b = 1$, and $c = -\frac{45}{4}$.

Now, plug these values into the quadratic formula:

$x = \frac{-1 \pm \sqrt{1 - 4 \cdot 8 \cdot \left(-\frac{45}{4}\right)}}{2 \cdot 8}$

Simplify inside the square root:

$x = \frac{-1 \pm \sqrt{1 + 45 \cdot 2}}{16}$

$x = \frac{-1 \pm \sqrt{91}}{16}$

So, the solutions to the second equation are:

$x = \frac{-1 + \sqrt{91}}{16}$ and $x = \frac{-1 - \sqrt{91}}{16}$