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
Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`
Solve : 3(2x + 1) - 2x+2 + 5 = 0.
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Simplify : −3 (1 − x2) − 2{x2 − (3 − 2x2)}
Simplify : `2{m-3(n+overline(m-2n))}`
Write each of the following in the simplest form:
(a3)5 x a4
Write each of the following in the simplest form:
a2 x a3 ÷ a4
Write each of the following in the simplest form:
a-3 x a2 x a0
Simplify the following:
`(27 xx^9)^(2/3)`
Simplify the following:
`((64"a"^12)/(27"b"^6))^(-2/3)`
