xa=yb=zc and y2=xz. Find b.

Options
- 2ac/a+c
- x(a+c)/yz
- a+c/ac
- acxyz

CORRECT ANSWER : 2ac/a+c

Discussion Board
solution

x^a = y^b = z^c and y^2 = xz
y^b = x^a
y = x^a/b

z^c = x^a
z = x^a/c

Now,
y^2 = xz
x^2(a/b) = x.x^a/c
x^2a/b = x^1+a/c [since x^a.x^b = x^a+b, ".=multiply]
since bases are same, equate the powers
2a/b = 1+a/c
2a/b = c+a/c
b = 2a/c+a/c
b = 2ac/c+a

Asrita Koppisetti 08-7-2023 07:50 AM

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