Answer

2a+3b = 12
(1)

Square both sides

(2a+3b)^2 = 100

Expand the LHS

4a^2+9b^2 +6\cdot 2ab = 100

then,

4a^2+9b^2 = 144-6\cdot 2ab = 144-6\cdot 9 =90

that is

4a^2+9b^2 = 90
(2)

Construct an equation using the conjugate of 2a+3b

(2a+3b)^2+(2a-3b)^2=2(4a^2+9b^2)

Substituting (1) and (2) results in

(2a-3b)^2 =2(4a^2+9b^2) - (2a+3b)^2

= 2\cdot 90-12^2 = 36

Therefore

The value of |2a-3b| is 6

Steven Zheng posted 1 hour ago

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