A and B are positive acute angles such that 2 B=3 ^2 A and 3 2 A=2 2 B . What is the value of (A+2 B) ?

Step-by-step solution

From question, we have 2 B=3 ^2 A and 3 2 A=2 2 B Now, aligned & (A+2 B)= A 2 B- A 2 B & = A 3 ^2 A- A 3 2 2 A aligned aligned & =3 A ^2 A- 3 2 A (2 A- A) & =3 A ^2 A-3 A ^2 A=0 & (A+2 B)= ( 2 ) & A+2 B= 2 aligned