Question

2a=3+2b prove that 8a3-8b3-36ab=27

Answer 1

by cubing both sides,
(2a)³=(3+2b)³
or,8a³=(3)³+(2b)³+3×3×2b(3+2b)
or,8a³=27+8b³+18b×2a
or,8a³=27+8b³+36ba
or,8a³-8b³-36ba=27
,hence proved.

Answer 2

The relation between a and b is true.

Given: The equation = 2a = 3+2b.

To Prove: $8a^{3} -8b^{3} -36ab=27.$

Solution:

2a = 3+2b

2a-2b = 3

Cube both the sides.

$(2a-2b)^{3}=3^{3}$

Identity: $(x-y)^{2} =x^{3} -y^{3} -3xy(x-y)$.

Using the identity in the equation.

-$8a^{3} -8b^{3}-3(2a)(2b)(2a-2b)=27$

$8a^{3} -8b^{3}-12ab(2a-2b)=27$

Put the value of 2a-2b = 3 i the equation.

$8a^{3} -8b^{3}-12ab(3)=27$

$8a^{3} -8b^{3}-36ab=27$

Hence Proved.

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