Question

X=cy+bz y=az+cx z=ax+by then prove that x^2/1-a^2=y^2/1-b^2=z^2/1-c^2

Answer 1

Answer:

Step-by-step explanation:

Let us eliminate  z  from first two equations.

As x = cy + b(ax+by) = cy + b²x + aby.

and multiplying each term by x, we get

x² = cxy + b²x²+  abxy. ----------------- [1]

and similarly y = az + cx = a(bx+ay) + cx = abx + a²y + cx

and multiplying each term by y, we get

y² = abxy + a²y² + cxy. ---------------  [2]

subtracting from [2] from [1], we have

x² - y² = b²x² - a²y²

x² - b²x² = y² - a²y²

x²(1 - b²) = y²(1  - a²)

x²/1 - a² = y²/ 1 - b².

Similarly we can eliminate x from equations for y and z to get

y²/ 1 - b² = z²/ 1 - c²

and hence x²/1 - a² = y²/ 1 - b² = z²/ 1 - c²