Solve the following pair of simultaneous equations.
2+5 =21 & x + =3
Answers
Answer:
3
x
+
6
x+y
=3⇒
6
2x+x+y
=3⇒3x+y=18 ...(i)
3
y
−
2
x−y
=6⇒
6
2y−3x+3y
=6⇒−3x+5y=36 ...(ii)
On adding (i) and (ii), we get
3x+y=18
−3x+5y=36
6y=54
∴y=9
On putting y=9 in (i), we get
3x+9=18⇒3x=9⇒x=3
∴x=3,y=9
Step-by-step explanation:
Answer:
We will make use of the following identities to solve the question :
(a+b)
2
+(a−b)
2
=2(a
2
+b
2
)⟶(1)
(a+b)
3
+(a−b)
3
=2a(a
2
+3b
2
)⟶(2)
Now, given x=
2
5−
21
∴
x
1
=
5−
21
2
=
(5−
21
)(5+
21
)
2(5+
21
)
=
4
2(5+
21
)
⇒
x
1
=
2
5+
21
Now, x+
x
1
=
2
5−
21
+
2
5+
21
=5
Similarly, x
2
+
x
2
1
=(
2
5−
21
)
2
+(
2
5+
21
)
2
Using equation (1) we can easily write
x
2
+
x
2
1
=2×(
4
25
+
4
21
)=23
Also, x
3
+
x
3
1
=(
2
5−
21
)
3
+(
2
5+
21
)
3
Using equation (2),
x
3
+
x
3
1
=2×
2
5
×(
4
25
+
4
63
)=110
∴ (x
3
+
x
3
1
)−5(x
2
+
x
2
1
)+(x+
x
1
)=110−5×23+5=115−115=0