Question

If the mean of two numbers is 30 and the geometric mean is 24 then what will be these two numbers

Answer 1

Answer:

the numbers are 12 and 48

Step-by-step explanation:

let the numbers be a and b

mean = (a+b)/2 = 30

geometric mean = √a×b = 24

$\frac{a + b}{2} = 30 \\ a + b = 60 \\ a = 60 - b \: \: \: \: \: \: \: \: equ \: (1) \\ \\ geometric \: mean\\ \sqrt{ab} = 24 \\ squaring \: on \: both \: sides \\ ab = 24 \times 24 \\ ab = 576 \\ substitute \: a \: from \: equ \: (1) \\ (60 - b) \times b = 576 \\ 60b - {b}^{2} - 576 = 0 \\ {b}^{2} - 60b + 576 = 0 \\ {b}^{2} - 12b - 48b + 576 = 0 \\ b(b - 12) - 48(b - 12) = 0 \\ (b - 12)(b - 48) = 0 \\ b - 12 = 0 \: \: \: \: \: \: \: \: \: b - 48 = 0 \\ b = 12 \: \: or \: b = 48 \\ substitute \: b \: in \: equ \: (1) \\ a = 60 - b \\ a = 60 - 12 = 48$