Question

√25x+75 +3√x-2 =2+4√x-3 +√9x-18

Answer 1

Explanation:

`\large \boldsymbol{ \boxed{√(a)\cdot √(b)=√(a\cdot b) }} \\\\\\ √(25x+75) +3√(x-2) =2+4√(x-3) +√(9x-18) \\\\ √(25) \cdot √(x+3)+3√(x-2) =2+4√(x-3) +√(9)\cdot √(x-2) \\\\5√(x+3) +3√(x-2) \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4√(x-3) +3√(x-2) \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5√(x+3))^2 =(2+4√(x-3) )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5√(t) \ \big)^2=(2+√(t-6) )^2 \\\\`
`\large \boldsymbol{} 25t=4+16√(t-6) +16(t-6) \\\\(9t+92)^2=(16√(t-6) )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions`