If a and b are integers of opposite signs such that $(a + 3)^{2} : b^{2} = 9 : 1$ and $(a -1)^{2}:(b - 1)^{2} = 4:1$, then the ratio $a^{2} : b^{2}$ is
Option: 4
Explanation:Since the square root can be positive or negative we will get two cases for each of the equation.
For the first one,
a + 3 = 3b .. i
a + 3 = -3b ... ii
For the second one,
a - 1 = 2(b -1) ... iii
a - 1 = 2 (1 - b) ... iv
we have to solve i and iii, i and iv, ii and iii, ii and iv.
Solving i and iii,
a + 3 = 3b and a = 2b - 1, solving, we get a = 3 and b = 2, which is not what we want.
Solving i and iv
a + 3 = 3b and a = 3 - 2b, solving, we get b = 1.2, which is not possible.
Solving ii and iii
a + 3 = -3b and a = 2b - 1, solving, we get b = 0.4, which is not possible.
Solving ii and iv,
a + 3 = -3b and a = 3 - 2b, solving, we get a = 15 and b = -6 which is what we want.
Thus, $\frac{a^2}{b^2} = \frac{25}{4}$
