suppose x is non zero and let x 1y a show that 7y215y60 if 6

suppose x is non zero, and let x= 1/y

a. show that 7y²-15y+6=0 if 6x²-15x+7=0 and vice versa

b.more generally show that cy²+by+a=0 if ax²+bx+c=0 and vice versa

a. show that 7y2-15y+6=0 if 6x2-15x+7=0 and vice versa

7y^2-15y+6=0

plug y = 1/x in the above equation:

7(1/x)^2 -15(1/x) +6 =0

take x^2 as lcd :

7 -15x +6x^2 =0

6x^2 -15x +7 =0

Hence Proved

b.more generally show that cy2+by+a=0 if ax2+bx+c=0 and vice versa

cy^2+by+a=0

Plug y = 1/x

c(1/x)^2 +b(1/x) +a =0

take x^2 as lcd :

ax^2 +bx +c =0

Hence proved