Advertisements
Advertisements
प्रश्न
If `a=xy^(p-1), b=xy^(q-1)` and `c=xy^(r-1),` prove that `a^(q-r)b^(r-p)c^(p-q)=1`
Advertisements
उत्तर
It is given that `a=xy^(p-1), b=xy^(q-1)` and `c=xy^(r-1)`
`thereforea^(q-r)b^(r-p)c^(p-q)`
`=(xy^(p-1))^(q-r)(xy^(q-1))^(r-p)(xy^(r-1))^(p-q)`
`=x^((q-r))y^((p-1)(q-r))x^((r-p))y^((r-p)(q-1))x^((p-q))y^((p-q)(r-1))`
`=x^((q-r))x^((r-p))x^((p-q))y^((p-1)(q-r))y^((r-p)(q-1))y^((p-q)(r-1))`
`=x^((q-r)+(r-p)+(p-q))y^((p-1)(q-r)+(r-p)(q-1)+(p-q)(r-1))`
`=x^(q-r+r-p+p-q)y^(pq-q-pr+r+rq-r-pq+p+pr-p-qr+q)`
`=x^0y^0`
= 1
Hence proved.
APPEARS IN
संबंधित प्रश्न
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Simplify:
`(16^(-1/5))^(5/2)`
Show that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Show that:
`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
If \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\] then x =
If \[\sqrt{2^n} = 1024,\] then \[{3^2}^\left( \frac{n}{4} - 4 \right) =\]
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
