Question

if 3m + 4n = 4 and 3m - 4n = 3, find the
values of:
(i) 18m^2 + 32^n
(ii) 96mn
(iii) 9m^2 - 16n^2
​

Answer 1

3m+4n = 4

3m-4n = 3

Adding both equations

6m = 7

m = 7/6------(1)

Putting value of m in any above equation

3(7/6)+4n = 4

4n = 4-7/2

4n = 1/2

n = 1/8------(2)

Putting values of mn in given problems

(i) 18(7/6)²+32(1/8)²

18×49/36 + 32×1/64

= 25

(ii) 96(7/6)(1/8)

= 14

(iii)9(7/6)²-16×(1/8)²

9×49/36 - 16×1/64

12.25 - 0.25

= 12

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