Question

if x^a.x^b.x^c=1 then show x^(a^2/bc).x^(b^2/ca).x^(c^2/ab)=x^3

Answer 1

${x}^{a} \times {x}^{b} \times {x}^{c} = 1 \\ {x}^{a + b + c} = {x}^{0} \\ a + b + c = 0$
To prove
${x}^{ \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ac} + \frac{ {c}^{2} }{ab} } = {x}^{3} \\ or \\ \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ac} + \frac{ {c}^{2} }{ab} = 3 \\ = \frac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc}$
But since a+b+c is zero, therefore
${a}^{3} + {b}^{3} + {c}^{3} = 3abc$
Simplifying, we get
$= \frac{3abc}{abc} \\ = 3$
Hence proved..
Mark it as the brainliest answer