Question

from the equation 4√5x^2 + 7x - 3√5 =0, the value of x will be​

Answer 1

$4\sqrt{5}x^{2} + 7x - 3\sqrt{5} = 0$

Product of 4√5 and 3√5 is 60,  So find two suitable numbers, whose product is 60 and their difference be 7.

(12 and 5 are suitable numbers)

$4\sqrt{5}x^{2} + 7x - 3\sqrt{5} = 0\\\\4\sqrt{5}x^{2} + (12-5)x - 3\sqrt{5}= 0\\\\4\sqrt{5}x^{2} + 12x - 5x - 3\sqrt{5} = 0\\\\4x(\sqrt{5}x + 3) - \sqrt{5}(\sqrt{5}x + 3) = 0\\ \\(\sqrt{5}x + 3) (4x - \sqrt{5}) = 0\\\\x = -3/\sqrt{5}\\ x = \sqrt{5}/4$

Hence, the roots of the equation are ,  -3/√5 and √5/4