Progressive variables
Algebra
Level
2
If a,b,c are in A.P ,x is GM of a and b while y is GM of b and c, then b^2 is:
Details:Where AM: Arithmetic mean, GM: Geometric mean, HM: Harmonic mean
HM of x^2 and y^2
GM of x^2 and Y^2
AM of x^2 and y^2
None of These
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If a , b , c are in AP then a-b=b-c; from here we get 2b=a+c; ...............................(1)equ
x is the AM of a & b; then x= sqrt(ab); x^2=ab;........................................................(2)equ
y is the AM of b & c ; then y= sqrt(bc); y^2=bc;.......................................................(3)equ
by option checking => AM of x^2+y^2=(ab+bc)/2;
=b(a+c)/2;......................................................(4)equ
from equ (1) we get (a+c)/2=b;
on putting the value of (a+c)/2; in equ (4) we have
AM of x^2+y^2= b^2.