\sqrt{ x^(2)-10x+25}+25+12√(x) =15√(x)

Question

`\sqrt{ x^(2)-10x+25}+25+12√(x) =15√(x)`

Answer 1

Explanation:

`\sqrt{ x^(2)-10x+25}+25+12√(x) =15√(x) \\ \\ \therefore \: \sqrt{ x^(2)-10x+ {5}^(2) }+25 =15√(x) - 12√(x)\\ \\ \therefore \: \sqrt{( x - 5)^(2)}+25 =3√(x) \\ \\ \therefore \: x - 5+ 25 = 3 √(x) \\ \\ \therefore \: x + 20 = 3 √(x) \\ \\ squaring \: both \: sides \\ (x + 20)^(2) = ( {3 √(x) })^(2) \\ \therefore \: {x}^(2) + 40x + 400 = 9x \\ \therefore \: {x}^(2) + 40x + 400 - 9x = 0 \\ \therefore \: {x}^(2) + 31x + 400 = 0 \\`