Question

11. The A.M. of two positive numbers is 40 and their G. M. is 24. The numbers are
(a) (72,8)
(b) (70, 10)
(c) (60,20) 24 = 727
(d) none of these
​

Answer 1

Answer:

a) (72,8)

Step-by-step explanation:

Complete solution AM= (a+b)/2 40= (a+b)/2 80=a+b 80-b=a......(1) GM=square root of a×b 24=square root of a×b by squaring both sides 576= a×b from equation (1) 576=(80-b)b 576=80b-square of b by transposing square of b - 80b - 576= 0 square of b - 72b - 8b -576 =0 b(b-72) -8(b-72)=0 (b-8) (b-72)= 0 either b-8=0 or b-72=0 b=8 b=72 then from eq. (1) then from eq .(1) a=80-8 a=80-72 a=72 a=8 {a,b}={72,8} {a,b}={8,72}