Question

if 2x+3y=21 and xy=15 then find value of i)4x^2+9y^2 ii)4x^2-9y^2 iii)8x^3+27y^3iv)8x^3- 27y^3

Answer 1

Given. that,
2x+3y=21.............................1
and xy=15...........................2
eq1 can be written as,
x=(21-3y)/2..........................3
putting eq3 in eq2 we get,
(21-3y)/2×y=15
21y-3y^2=30
y^2-7y+10=0
(y-5)(y-2)=0
y=5 or y=2
for y=5,we get
x=3
and for y=2,we get
x=15/2
Therefore pairs of solution we have,
(3,5),(15/2,2)
i)4x^2+9y^2
for x=3 and y=5
=4x^2+9y^2
=4×3^2+9×5^2
=36+225
=261
for x=15/2 and y=2
=4x^2+9y^2
=4×(15/2)^2+9×2^2
=225+36=261
ii)4x^2-9y^2
for x=3 and y=5
=4x^2-9y^2
=4×3^2-9×5^2
=36-225
=-189
for x=15/2 and y=2
=4x^2-9y^2
=4×(15/2)^2-9×2^2
=189. ( here this will be positive)
iii)8x^3+27y^3
for x=3 and y=5
=8×3^3+27×5^3
=216+3375
=3591
for the pair (15/2,2) also this value will be same.
iv)8x^3-27y^3
for x=3 and y=5
=8×3^3-27×5^3
=-3159
for the pair of (15/2,2) answer will be positive i.e 3159.

Answer 2

2+3=13 =6

(2+3)

3

=13

3

8

3

+27

3

+3×4

2

×3+3×2×9

2

=13

3

8

3

+27

3

+18(2+3)=13

3

8

3

+27

3

+18(6)(13)=13

3

8

3

+27

3

=793