If a and b are integers of opposite signs such that $$(a + 3)^{2} : b^{2} = 9 : 1$$ and $$(a -1)^{2}:(b - 1)^{

Question

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

Accepted Answer

25:4. 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,

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

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

If a and b are integers of opposite signs such that (a+3)2:b2=9:1(a + 3)^{2} : b^{2} = 9 : 1(a+3)2:b2=9:1 and (a−1)2:(b−1)2=4:1(a -1)^{2}:(b - 1)^{2} = 4:1(a−1)2:(b−1)2=4:1, then the ratio a2:b2a^{2} : b^{2}a2:b2 is

If a and b are integers of opposite signs such that (a+3)2:b2=9:1(a + 3)^{2} : b^{2} = 9 : 1(a+3)2:b2=9:1 and (a−1)2:(b−1)2=4:1(a -1)^{2}:(b - 1)^{2} = 4:1(a−1)2:(b−1)2=4:1, then the ratio a2:b2a^{2} : b^{2}a2:b2 is

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

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