Question

Quadratic equation grade :9
10 points;)​

Answer 1

Explanation:

put (x+2)/(x-2)=a

a-1/a=5/6

`multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\(x+2)/(x-2) =(3)/(2) \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\`

`or~3a+2=0\\a=-2/3\\(x+2)/(x-2) =-(2)/(3) \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5`

2.

put (x+3)/x=a

a+1/a=4 1/4

`a+(1)/(a) =(17)/(4) \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\(x+3)/(x) =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\(x+4)/(x) =(1)/(4) \\4x+16=x\\3x=-16\\x=-16/3`