If x(y+z)=32,y(z+x)=65,z(x+y)=77 then find the value of xyz
Farheena , 7 Years ago
Grade 12th pass
8 grade maths> If x(y+z)=32,y(z+x)=65,z(x+y)=77 then fin...
1 AnswersSubhash
Last Activity: 7 Years ago
x(y+z)=32
xy+xz=32 …...(1)
y(z+x)=65
yz+xy=65 …...(2)
z(x+y)=77
xz+xy=77 …..(3)
adding eq. 1,2&3--
2(xy+xz+yz)=174
xy+xz+yz=87 …..(4)
subs. eq. 1,2&3 from eq. 4 respectively, we get---
yz=55 …....(5)
xz=22 …...(6)
xy=10 …....(7)
therefore- z=55/y from eq. 5
and x=10/y from eq. 7
since xz=22 (eq. 6)
= 55/y * 10/y = 22
= 22 y2 = 55*10
= y2 = 550/22=25
y=5
x= 10/y = 10/5= 2
z= 55/y = 55/5 = 11
therefore-- xyz = 2*11*5 =110
therefore-- xyz=110
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