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Question
Find the square of `5-x+2/x`
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Solution
`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
- (5)2 = 25
- (−x)2 = x2
- `(2/x)^2=4/x^2`
- 2(5)(−x) = −10x
- 2(−x) `(2/x) = 2 xx -1xx2=-4`
- `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`
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