Advertisements
Advertisements
Question
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
Solution
`sqrt(a/b)=(b/a)^(1-2x)`
`rArr(a/b)^(1/2)=(a/b)^(-(1-2x))`
`rArr1/2=-(1-2x)`
`rArr1/2=2x - 1`
`rArr1/2+1=2x`
`rArr1/2+(1xx2)/(1xx2)=2x`
`rArr1/2+2/2=2x`
`rArr(1+2)/2=2x`
`rArr3/2=2x`
`rArrx=3/4`
APPEARS IN
RELATED QUESTIONS
Prove that:
`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
Prove that:
`(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=16/3`
If `5^(3x)=125` and `10^y=0.001,` find x and y.
If 24 × 42 =16x, then find the value of x.
If (x − 1)3 = 8, What is the value of (x + 1)2 ?
The seventh root of x divided by the eighth root of x is
If 9x+2 = 240 + 9x, then x =
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.
If \[x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}\] and \[y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}\] then x + y +xy=
