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 ?->(Show Answer!)

1. 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

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By: anil on 05 May 2019 02.29 am

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, $$frac{a^2}{b^2} = frac{25}{4}$$

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