Question

If3m+4n=4 and3m-4n=3 find thne value of:
18m^2+32n^2

Answer 1

Step-by-step explanation:

Given--->

3 m + 4n = 4 .....................(1)

3 m - 4 n = 3 .....................(2)

To find ---> Value of ( 18m² + 32n² )

Solution---> Adding equation ( 1 ) and (2) , we get

3m + 4n + 3m - 4n = 4 + 3

+4n and (-4n ) cancel out each other

=> 6m = 7

=> m = 7 / 6

Subtracting equation(1)and(2) , we get

3m + 4n - ( 3m - 4n ) = 4 - 3

=> 3m + 4n - 3m + 4n = 1

3m and (-3m ) cancel out each other

=> 8 n = 1

=> n = 1 / 8

Now , 18m² + 32n² = 18 ( 7 / 6 )² + 32 ( 1 / 8 )²

= 18 × ( 49/36 ) + 32 × (1/64))

= 49 / 2 + 1 / 2

= ( 49 + 1 ) / 2

= 50 / 2

18m² + 32n² = 25

Answer 2

Question :---- we have to find value of 18m² + 32n² ?

Given :-----

• 3m + 4n = 4
• 3m - 4n = 3

Solution :--------

Let ,

3m + 4n = 4 -------------- Equation (1)

3m - 4n = 3 -------------- Equation (2)

Adding both Equation now we get,

6m = 7

m = 7/6

Putting value of m in any Equation now we get,,

3×(7/6) + 4n = 4

4n = 4 - (7/2)

4n = 1/2

n = 1/8

______________________________

Now putting value of m & n Question now we get,

18m² + 32n²

= 18(7/6)² + 32(1/8)²

= 18(49/36) + 32(1/64)

= 49/2 + 1/2

= 50/2

= 25 (Ans)

(Hope it helps you)