Advertisements
Advertisements
प्रश्न
Prove that: `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`
Advertisements
उत्तर
`a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`
L.H.S. = `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1)`
= `(1/a)/(1/a + 1/b) + (1/a)/(1/a - 1/b)`
= `(1/a)/((b + a)/(ab)) + (1/a)/((b - a)/(ab))`
= `1/a xx (ab)/(b+ a) + 1/a xx (ab)/(b - a)`
= `b/( b + a ) + b/(b - a)`
= `( b^2 - ab + b^2 + ab )/( b^2 - a^2 )`
= `( 2b^2 )/( b^2 - a^2 )`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Solve : 3(2x + 1) - 2x+2 + 5 = 0.
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Simplify: a5 ÷ a3 + 3a × 2a
Simplify: (y3 − 5y2) ÷ y × (y − 1)
Simplify the following and express with positive index:
3p-2q3 ÷ 2p3q-2
Simplify the following:
`(27 xx^9)^(2/3)`
Simplify the following:
`(8 xx^6y^3)^(2/3)`
Simplify the following:
`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`
Simplify the following:
`(2^"m" xx 3 - 2^"m")/(2^("m" + 4) - 2^("m" + 1)`
Simplify the following:
`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`
