Question

If 4a^2+3b^2/4a^2-3b^2 = 7/2 find 2a^4-11b^4/2a^4+11b^4

Answer 1

Given: 4a^2+3b^2 / 4a^2-3b^2 = 7/2

To find: The value of 2a^4-11b^4 / 2a^4+11b^4

Solution:

• Now we have given 4a^2+3b^2 / 4a^2-3b^2 = 7/2

• Using componendo and dividendo, we get:

              4a^2+3b^2+4a^2−3b^2 / 4a^2+3b^2-4a^2+3b^2 = 7+4 / 7-4

              8a^2 / 6b^2 = 11/3

              4a^2/b^2 = 11

              a = ±√11 b / 2

• Now consider +√11 b/2, we get:

              2(√11 b/2)^4-11b^4 / 2(√11 b/2)^4+11b^4

              121b^4 - 88b^4 / 121b^4 + 88b^4

              33b^4 / 209b^4

              33/209

              3/19

• Now consider -√11 b/2, we get:

               2(-√11 b/2)^4-11b^4 / 2(-√11 b/2)^4+11b^4

              121b^4 - 88b^4 / 121b^4 + 88b^4

              33b^4 / 209b^4

              33/209

              3/19

Answer:

            So the value of 2a^4-11b^4/2a^4+11b^4 is 3/19.