Question

Find the square of `5-x+2/x`

Answer 1

`5-x+2/x`

(x + y + z) 2 = x² + y² + z² + 2xy + 2yz + 2zx

`x=5, y=-x, z= 2/x`

Apply the formula

`(5-x+2/x)^2 = (5)^2 + (-x)^2+(2/x)^2 + 2(5)(-x)+2(-x)(2/x) +2(5) (2/x)`

Simplify each term

1. (5)² = 25
2. (−x)² = x²
3. `(2/x)^2=4/x^2`
4. 2(5)(−x) = −10x
5. 2(−x) `(2/x) = 2 xx -1xx2=-4`
6. `2(5) (2/x)=20/x`

Combine all terms

`(5-x+2/x)^2 = 25+x^2+4/x^2-10x-4+20/x`

Combine like terms

`x^2 + 25-4-10x+20/x+4/x^2`

`x^2+21-10x+20/x+4/x^2`