Advertisements
Advertisements
प्रश्न
Prove that:
`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`
Advertisements
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:
`9^0xx4^-1÷2^-4`
Simplify:
`[(64)^-2]^-3÷[{(-8)^2}^3]^2`
Evaluate:
`(8+4+2)^0`
Simplify:
`15"y"^8÷3"y"^3`
Simplify:
`(2"x"^2"y"^-3)^-2`
Simplify:
`(-2"x"^(2/3)"y"^(-3/2))^6`
Simplify and express as positive indice:
`("a"^(-2)"b")^(1/2)xx("a""b"^-3)^(1/3)`
Show that:
`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`
Evaluate:
`("a"^(2"n"+1)xx"a"^((2"n"+1)(2"n"-1)))/("a"^("n"(4"n"-1))xx("a"^2)^(2"n"+3)`
Simplify:
`("x"^(2"n"+7).("x"^2)^(3"n"+2))/"x"^(4(2"n"+3)`
