Question

Find the relation between x, y & z.
${36}^{x} = {48}^{y} = {64}^{z}$
​

Answer 1

Let the point P(x,y) is equidistant from the points A(3,6)and B(−3,4)

∴PA=PB

By using the distance formula

=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

we have

⇒

(x−3)

2

+(y−6)

2

=

(x+3)

2

+(y−4)

2

⇒(x−3)

2

+(y−6)

2

=(x+3)

2

+(y−4)

2

⇒x

2

−6x+9+y

2

−12y+36=x

2

+6x+9+y

2

−8y+16

⇒−6x−6x−12y+8y+36−16=0

⇒−12x−4y+20=0

⇒3x+y−5=0

Hence this is a relation between x and y.