A #B=A+ (A - B)2 and C & D = 3 x (C+ D), then The value of (2 & 3) #7
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Answer:
It is given that a:(b+c)=1:3 and c:(a+b)=5:7 and we solve these expressions as follows:
b+c
a=
3
1
⇒3a=b+c
⇒3a−b=c....(1)
a+b
c=
7
5
⇒7c=5(a+b)
⇒7c=5a+5b....(2)
Multiplying the first equation by 7 we get:
7(3a−b)=7c
⇒7c=21a−7b....(3)
Now, subtracting equation 2 from equation 3, we have:
7c−7c=(21a−7b)−(5a+5b)
⇒0=21a−7b−5a−5b
⇒16a=12b
⇒b= 12
16a
⇒b= 3
4a
Substituting the value of b in equation 1:
3a−
3
4a
=c
⇒c=
3
9a
−
3
4a
⇒c=
3
9a−4a
⇒c=
3
5a
Now, lets find the value of b:(a+c) as shown below:
a+c
b
=
a+
3
5a
3
4a
=
3
3a
+
3
5a
3
4a
=
3
8a
3
4a
=
3
4a
×
8a
3
=
8a
4a
=
2
1
=1:2
hence, b:(a+c)=1:2.
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