Question

27 , x , y , 79 z
find value x y and z​

Answer 1

Answer:

Given equations are xy+x+y=23

⇒x(y+1)=23−y

⇒x=

y+1

23−y

(i),

yz+y+z=27

⇒z(y+1)=27−z

⇒z=

y+1

27−y

ii)

and xz+x+z=41 .(iii)

Substituting (i) and (ii), we get

(

y+1

23−y

)(

y+1

27−y

)+

y+1

23−y

+

y+1

27−z

=41

⇒

(y+1)

2

621+y

2

−50y

+

y+1

50−2y

=41

⇒

(y+1)

2

621+y

2

−50y+(50−2y)(y+1)

=41

⇒621+y

2

−50y+50y−50−2y

2

−2y=41y

2

+41+82y

⇒42y

2

+84y−630=0

⇒y

2

+2y−15=0

⇒y

2

−3y+5y−15=0

⇒y(y−3)+5(y−3)=0

⇒(y+5)(y−3)=0

⇒y=−5,3

Substituting y in (i), we get

⇒x=−7,5

Substituting y in (ii), we get

⇒z=−8,6