Grade 12th passAlgebra
if x,y,z are positive numbers and xy + x + y = 23 ; xz + x + z = 41; yz + y + z = 27, find x + y + z
if x,y,z are positive numbers and xy + x + y = 23 ; xz + x + z = 41; yz + y + z = 27, find x + y + z
1 Answer
Sunil Raikwar
xy + x + y = 23
xy+x+y+1=24
(x+1)(y+1)=24..........................1
xz + x + z = 41
xz + x + z + 1 = 42
(x+1)(z+1) = 42..............2
yz + y + z +1 = 28
(y+1)(z+1) = 28...................3
from 1, 2 & 3 ony x=5,y=3 and z=6 satisfy the given equations therefore
x + y + z=14
xy+x+y+1=24
(x+1)(y+1)=24..........................1
xz + x + z = 41
xz + x + z + 1 = 42
(x+1)(z+1) = 42..............2
yz + y + z +1 = 28
(y+1)(z+1) = 28...................3
from 1, 2 & 3 ony x=5,y=3 and z=6 satisfy the given equations therefore
x + y + z=14
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago