Answer:
The value of x in the equation x² + (x+7)² = (x+9)² is x = (4,8).
Step-by-step explanation:
It is given that, the equation x² + (x+7)² = (x+9)² is to be solved.
Now,
Let us expand the equation by using the formula of (a + b)², that is;
(a + b)² = a² + 2ab + b²
So,
=> x² + (x+7)² = (x+9)²
=> x² + (x² + 2.7x + 7²) = (x² + 2.9x + 9²)
=> x² + x² + 14x + 49 = x² + 18x + 81
=> x² + 14x - 18x + 49 - 81 = 0
=> x² - 4x - 32 = 0
Further, let's factorize the equation obtained;
=> x² - 4x - 32 = 0
=> x² - (8 - 4)x - 32 = 0
=> x² - 8x + 4x - 32 = 0
=> x(x - 8) + 4(x - 8) = 0
=> (x - 8) (x - 4) = 0
Now, on comparing the two factors obtained above;
=> x - 8 = 0
=> x = 8
and
=> x - 4 = 0
=> x = 4
Therefore, the values of x in the equation x² + (x+7)² = (x+9)² is x = (4,8).
To know more about this topic, click here:
https://brainly.com/question/19297665
#SPJ9
