Question

please answer this question ​

Answer 1

ax _a² +bx _b²

____________ = 2

x² _ax _bx +ab

ax _ a² +bx _b² = 2x² _2ax _ 2bx +2ab

2x² +a² + b² _3ax _3bx +2ab =0

Answer 2

$</p><p></p><p> \bf \implies \: \frac{a(x - a) + b(x - b)}{(x - b)(x - a)} = 2 \\ \bf \implies \frac{ax - {a}^{2} + bx - {b}^{2} }{(x - a)(x - b)} = 2 \\ \bf \implies \: ax - {a}^{2} + bx - {b}^{2} = 2(x - a)(x - b) \\ \bf \implies ax - {a}^{2} + bx - {b}^{2} = 2( {x}^{2} - ax - bx + ab) \\ \bf \implies \: ax + bx - {a}^{2} - {b}^{2} = 2 {x}^{2} - 2ax - 2bx + 2ab \\ \bf \implies \: 2 {x}^{2} - 3ax - 3bx + 2ab + {a}^{2} + {b}^{2} = 0 \\ \bf \implies \: 2x - 3x(a + b) + {(a + b)}^{2} = 0 \\ \bf \implies \: 2 {x}^{2} - 2x(a + b) - x(a + b) + {(a + b)}^{2} = 0 \\ \bf \implies \: 2x [x - (a + b) \: ] - (a + b)[x - (a + b)] \: = 0 \\ \bf \implies \: [2x - (a + b)][x - (a + b)] \: = 0 \\ \bf \implies \: 2x = a + b \\ \bf \implies x = \frac{a + b}{2}$