the difference between two number is 3. Write the data in form of linear equation in two variables. Also, represent it graphically.If smaller number is 8, then find graphically the value of larger number.
Answers
x - 8 = 3
x = 3 + 8
x = 11
So, therefore, the numbers are 8 and 11
Step-by-step explanation:
11 is the answer
X=11+y+z=6
xy+yz+zx=12
2) We know that,
\begin{lgathered}{(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx) \\ = > {6}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2 \times 12 \\ = > {x}^{2} + { y }^{2} + {z}^{2} = 36 - 24 = 12\end{lgathered}
(x+y+z)
2
=x
2
+y
2
+z
2
+2(xy+yz+zx)
=>6
2
=x
2
+y
2
+z
2
+2×12
=>x
2
+y
2
+z
2
=36−24=12
3) And,
We also know that,
\begin{lgathered}{x}^{3} + {y}^{3} + {z}^{3} - 3xyz = (x + y + z) \\ \times ( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx) \\ = > 6 \times (12 - 12) = 0 \\ = > {x}^{3} + {y}^{3} + {z}^{3} - 3xyz = 0 \\ = > {x}^{3} + {y}^{3} + {z}^{3} = 3xyz\end{lgathered}
x
3
+y
3
+z
3
−3xyz=(x+y+z)
×(x
2
+y
2
+z
2
−xy−yz−zx)
=>6×(12−12)=0
=>x
3
+y
3
+z
3
−3xyz=0
=>x
3
+y
3
+z
3
=3xyz
Hence Proved.