Advertisements
Advertisements
प्रश्न
Prove that:
`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`
उत्तर
`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`
`"L"."H"."S".=1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a")`
`=1/("x"^("a"-"a")+"x"^("a"-"b"))+1/("x"^("b"-"b")+"x"^("b"-"a")`
`=1/("x"^"a"."x"^-"a"+"x"^"a"."x"^-"b")+1/("x"^"b"."x"^-"b"+"x"^"b"."x"^-"a"`
`=1/("x"^"a"("x"^-"a"+"x"^-"b"))+1/("x"^"b"("x"^-"b"+"x"^-"a")`
`=1/(("x"^-"a"+"x"^-"b")) [1/"x"^"a"+1/"x"^"b"]`
`=1/("x"^-"a"+"x"^-"b") ["x"^-"a"+"x"^-"b"]=1="R"."H"."S".`
APPEARS IN
संबंधित प्रश्न
Compute:
`(2^-9÷2^-11)^3`
Compute:
`(2/3)^(-4)xx(27/8)^-2`
Compute:
`(56/28)^0÷(2/5)^3xx16/25`
Compute:
`(625)^(-3/4)`
Compute:
`(27/64)^(-2/3)`
Compute:
`(-3)^4-(root(4)(3))^0xx(-2)^5÷(64)^(2/3)`
Simplify:
`8^(4/3)+25^(3/2)-(1/27)^(-2/3)`
Evaluate:
`(4"x")^0`
Evaluate:
`(7"x"^0)^2`
Simplify:
`5"z"^16÷15"z"^-11`
