Advertisements
Advertisements
प्रश्न
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
Advertisements
उत्तर
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
LHS = `(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)`
`=[x^((a-b)(a+b))][x^((b-c)(b+c))][x^((c-a)(c+a))]`
`=x^((a^2-b^2))x^((b^2-c^2))x^((c^2-a^2))`
`=x^(a^2-b^2+b^2-c^2+c^2-a^2)`
`=x^0`
= 1
= RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
`1/(1 + x^(b - a) + x^(c - a)) + 1/(1 + x^(a - b) + x^(c - b)) + 1/(1 + x^(b - c) + x^(a - c)) = 1`
Prove that:
`sqrt(3xx5^-3)divroot3(3^-1)sqrt5xxroot6(3xx5^6)=3/5`
Show that:
`(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1`
If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.
If a and b are different positive primes such that
`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.
Write the value of \[\sqrt[3]{7} \times \sqrt[3]{49} .\]
When simplified \[\left( - \frac{1}{27} \right)^{- 2/3}\] is
If \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\] then x =
If \[x + \sqrt{15} = 4,\] then \[x + \frac{1}{x}\] =
The positive square root of \[7 + \sqrt{48}\] is
