Advertisements
Advertisements
Question
If 2x = 3y = 12z, show that `1/z=1/y+2/x`
Advertisements
Solution
Let 2x = 3y = 12z = k
`rArr2=k^(1/x),` `3=k^(1/y),` `12=k^(1/z)`
Now,
`12=k^(1/z)`
`rArr2^2xx3=k^(1/z)`
`rArr(k^(1/x))^2xxk^(1/y)=k^(1/z)`
`rArrk^(2/x+1/y)=k^(1/z)`
`rArr2/x+1/y=1/z`
APPEARS IN
RELATED QUESTIONS
Simplify the following
`((x^2y^2)/(a^2b^3))^n`
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
Simplify:
`((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))`
Prove that:
`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
Find the value of x in the following:
`5^(x-2)xx3^(2x-3)=135`
\[\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^n - 2 \times 5^{n + 1}}\] is equal to
The value of \[\frac{\sqrt{48} + \sqrt{32}}{\sqrt{27} + \sqrt{18}}\] is
If `a = 2 + sqrt(3)`, then find the value of `a - 1/a`.
