x=0 y=1 ,x=1 y=3, x=2 y=a, x=b y=-3 find the value of a and b
Answers
Answer:
Answerx1 + y1 = 3
...(i)1x 2 +y 2 =160...(ii)
Solving equation (i)
x1 +y1 = 31
or,
xy
y+x = 31
or, x+y= 3 xy
...(iii)
Simplifying equation (ii)
x 2 +y 2 =160
or, x 2 +y 2 =160
or, x2 +y 2 +2xy−2xy=160 (x+y) 2
−2xy=160 [a
2
+b
2
+2ab=(a+b)
2
]
Putting the value of (x+y) from equation (iii)
(
3
xy
)
2
−2xy=160
or, (
3
xy
)
2
−2xy=160
or, (
3
xy
)
2
−2×
3
xy
×3+3
2
−3
2
−160=0
or (
3
xy
−3)
2
−9−160=0
or, (
3
xy
−3)
2
=169
or
3
xy
−3=±
169
or,
3
xy
−3=±13
when
3
xy
−3=+13
or,
3
xy
=13+3
or, xy=16×3
or, xy=48....(iv)
when
3
xy
−3=−13
or
3
xy
=−13+3
or, xy=−10×3
or, xy=−30...(v)
Hence, the solution of the given pair of equations
will be every pair of x & y which satisfies any
of the equation (iv) or (v)
So, there will be infinite solutions.
Step-by-step explanation:
You can refer to the attachment too ☺️
Given: y=a+ xb
a,b are constants
at x=−1,y=1a+ −1b =1⇒a−b=1→(1)
at x=−5,y=5
a+ −5 b =5⇒a− 5b
=5→(2)
(2)−(1)⇒
5
4b
=4⇒b=5,a=6
∴a+b=11