Question

(x-5)² - (x+2)² = 2
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Answer 1

Given: The equation is$(x-5)^{2} -(x+2)^{2}=2$.

We have to solve the given equation.

We are solving in the following way:

As we know that:

$=>(a+b)^{2}=a^{2} +2ab+b^{2}\\=>(a-b)^{2} =a^{2} -2ab+b^{2}$

By using the above statement, we are solving the given equation.

We have,

$(x-5)^{2} -(x+2)^{2}=2$

$=>(x-5)^{2}=x^{2} -10x+25\\=>(x+2)^{2} =x^{2} +4x+4$

Now,

$=>x^{2} -10x+25-x^{2} +4x+4=2\\=>-6x+29=2\\=>-6x=2-29\\=>-6x=-27\\\\=>x=\frac{27}{6}$

Solving the above equation further we get,

$=>x=\frac{27}{6}\\\\=>x=4.5$

Hence, the solution of the above equation will be$4.5$