(7x+2y)³ find the integers
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Answer:
Given, 7x+12y=220 ........(i)
Dividing by 7, we get
x+
7
12
y=
7
220
⇒x+y+
7
5y
=31+
7
3
⇒x+y+
7
5y−3
=31
We have to solve the equation for positive integers, so x and y are integers which ⇒
7
5y−3
= integer.
Multiplying by 3, we get
7
15y−9
= integer
⇒2y−1+
7
y−2
= integer
⇒
7
y−2
= integer
Let the integer be p.
7
y−2
=p
⇒y=7p+2 .......(ii)
Substituting y in (i),
7x+12(7p+2)=220
⇒7x+84p=196
⇒x=28−12p ......(iii)
So p can take any integral value , but from (iii), we see that x<0 fo p>2 which is not possible as we are solving the equation in positive integers.
So, p can be equal 0,1,2.
Substituting p in (ii), we get
⇒y=2,9,16
Substituting p in (iii), we get
⇒x=28,16,4
So, the solution set is {
x=28,16,4
y=2,9,16
.
Step-by-step explanation:
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Answered by
1
(7x+2y)³ find the integers
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(7x+2y)³
In this sum both number are integers.
All numbers are integers.
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