the h.m b/w two no is 16/5 their a.m is a and g.m. is g .if 2a+g^2=26 then find the no.
Answers
Answered by
19
LET THE NUMBERS BE X AND Y.
2XY/(X+Y)=16/5
10XY=16(X+Y)
XY=16(X+Y)/10------(1)
A.M-
X+Y/2=a
(X+Y)=2a-------(2)
G.M
g=√XY
g^2=XY--------(3)
PUTTING (1),(2),(3) IN THE GIVEN EQUATION
X+Y+XY=26
X+Y+16(X+Y)/10=26
We get X+Y=10 AND SO XY=16
SO X=16/Y
16/Y+Y=10
Y^2-10Y+16=0
(Y-8)(Y-2)=0
Y=8,2
ACCORDINGLY X=2,8
NUMBERS ARE 2 & 8
2XY/(X+Y)=16/5
10XY=16(X+Y)
XY=16(X+Y)/10------(1)
A.M-
X+Y/2=a
(X+Y)=2a-------(2)
G.M
g=√XY
g^2=XY--------(3)
PUTTING (1),(2),(3) IN THE GIVEN EQUATION
X+Y+XY=26
X+Y+16(X+Y)/10=26
We get X+Y=10 AND SO XY=16
SO X=16/Y
16/Y+Y=10
Y^2-10Y+16=0
(Y-8)(Y-2)=0
Y=8,2
ACCORDINGLY X=2,8
NUMBERS ARE 2 & 8
Similar questions