Question

please solve this equation in five minutes it is very very compulsory.please solve this problem​

Answer 1

Step-by-step explanation:

$\tt \bigg( \frac{ {x}^{a + b} }{ {x}^{c} } \bigg) ^{a - b} \times \bigg( \frac{x {}^{b + c} }{ {x}^{a} } \bigg) ^{b - c} \times \bigg( \frac{x {}^{c + a} }{ {x}^{b} } \bigg)^{c - a} \\ \dashrightarrow \tt \: ( {x}^{a + b - c} ) ^{a - b} \times ( {x}^{b + c - a} ) ^{b - c}\times ( {x}^{c + a - b} ) ^{c - a} \: \: \bigg [ \since \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \bigg] \\ \dashrightarrow \tt x ^{(a + b - c)(a - b)} \times {x}^{(b + c - a)(b - c)} \times {x}^{(c +a - b)(c - a) } \bigg[\since ( {x}^{a} ) ^{b} = x {}^{a \times b} = {x}^{ab} \bigg ] \\ \dashrightarrow \tt \: x {}^{( {a }^{2} - ab - ac - {b}^{2} + bc) } \times {x}^{ ({b}^{2} - ab - {c}^{2} + ac) } \times x ^{( {c}^{2} - bc - {a}^{2} + ab) } \\ \dashrightarrow \tt \: x {}^{( {a}^{2} - ab - ac - {b}^{2} + bc + {b}^{2} - ab - {c}^{2} + ac + {c}^{2} - bc - {a}^{2} + ab) } \bigg[\since {x}^{a} \times {x}^{b} = {x}^{(a + b)}\bigg ] \\ \dashrightarrow \tt {x}^{0} \\ \dashrightarrow \tt1$

Hence proved