Question

If x^2/4 + 16y^2+9z^2= 2xy+1.5xz+12yz then find x:y:z

Answer 1

x²/4 + 16y² + 9z² = 2xy +1.5 xz + 12yz

x² + 64y² + 36z² = 8xy +6xz + 48yz

x² +(8y)² + (6z)² = .(x )(8y) + (x)(6z) +(8y)(6z)

{x² + (8y)² + (6z)² -(x)(8y) -(x )(6z) -(8y)(6z)}=0

we know
a² + b² + c² - ab - bc -ca =0
but this is possible only when ,
a = b = c

but here a = x
b = 8y
c = 6z

so ,
x = 8y = 6z
x/48 = y/6 = z/8
x/24 = y/3 = z/ 4

so, x : y : z = 24 : 3 : 4

Answer 2

Answer:

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