If a is such a constant so that 9x^2 + 24x + a + 6x + x^2 is the square of a bionamal. What is a?
+128472 9x^2 + 24x + a + 6x + x^2 =
10x^2 + 30x + a
We need
( [sqrt 10] x + sqrt a ) ( [sqrt 10 ] x + sqrt a )
So that
2 sqrt (10 a) = 30
sqrt (10a) = 15 square both sides
10a = 225
a = 225 /10 = 22.5
Check
( [sqrt (10)x + sqrt (22.5) ] ^2 =
10x^2 + 2 ( sqrt 10 * sqrt 22.5 )x + 22.5 =
10x^2 + 2 sqrt (225) x + 22.5 =
10x^2 + 2 * 15x + 22.5 =
10x^2 + 30x + 22.5
