Solve 3^a = (b a^2)*(b-a^2) - Socratic AI (ScanMath)

Evaluate

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

Rewrite the expression

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

Swap the sides of the equation

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

Expand the expression

More Steps

a^{2} b^{2} - a^{4} b = 3^{a}

Move the expression to the left side

a^{2} b^{2} - a^{4} b - 3^{a} = 0

Substitute a= a^{2},b= - a^{4} and c= - 3^{a} into the quadratic formula b = \frac{- b \pm b ^{2} - 4 a c}{2 a}

b = \frac{a ^{4} \pm ( - a ^{4} ) ^{2} - 4 a ^{2} ( - 3 ^{a} )}{2 a ^{2}}

Simplify the expression

More Steps

b = \frac{a ^{4} \pm a ^{8} + 4 \times 3 ^{a} a ^{2}}{2 a ^{2}}

Simplify the radical expression

b = \frac{a ^{4} \pm a a ^{6} + 4 \times 3 ^{a}}{2 a ^{2}}

Separate the equation into 2 possible cases

b = \frac{a ^{4} + a a ^{6} + 4 \times 3 ^{a}}{2 a ^{2}} b = \frac{a ^{4} - a a ^{6} + 4 \times 3 ^{a}}{2 a ^{2}}

Simplify the expression

More Steps

b = \frac{a ^{3} + a ^{6} + 4 \times 3 ^{a}}{2 a} b = \frac{a ^{4} - a a ^{6} + 4 \times 3 ^{a}}{2 a ^{2}}

Solution

More Steps

b = \frac{a ^{3} + a ^{6} + 4 \times 3 ^{a}}{2 a} b = \frac{a ^{3} - a ^{6} + 4 \times 3 ^{a}}{2 a}

3^a = (b a^2)*(b A^2)