Question

Write two polynomials whose sum is x to the second power and whose difference is 1

Answer 1

Answer:

Therefore, the  first polynomial is:

$Z=\frac{1}{2}x^2+\frac{1}{2}$

the second polynomial is:

$Y=\frac{1}{2}x^2-\frac{1}{2}$

Step-by-step explanation:

We assume that: Z is first polynomial and Y is second polynomial.

Therefore, we have

$Z+Y=x^2\\\\Z-Y=1\\\\\implies Z+Y+Z-Y=x^2+1\\\\2Z=x^2+1\\\\Z=\frac{1}{2}x^2+\frac{1}{2}$

now, we get

$\implies Z+Y-Z+Y=x^2-1\\\\2Y=x^2-1\\\\Y=\frac{1}{2}x^2 -\frac{1}{2}$

Therefore, the  first polynomial is:

$Z=\frac{1}{2}x^2+\frac{1}{2}$

the second polynomial is:

$Y=\frac{1}{2}x^2-\frac{1}{2}$