I understand perfectly how to solve quadratic equations, but have come across a question which somewhat confuses me. I hope someone can help:
"Show that any root of the equation 5 + x - sqrt(3 + 4x) = 0 is also a root of the equation x^2 + 6x + 22 = 0. Hence show that the equation 5 + x - sqrt(3 + 4x) = 0 has no solutions."
What I don't understand is that it is obvious eq1 and eq2 have no solutions, so how can I possibly show that any roots of eq1 are also roots of eq2?
Thanks for the reply.
I can see that by squaring the original formula I get a quadratic:
x^2 - 4x + 22 = 0
But the question asks, "Show that any root of this equation...". I can't see that this equation has any roots...
Thanks, I'm glad someone agrees. I'm looking back over some A-Level maths (not done any in 7 years) and found this question in the 'past papers' part of an old book. I'm generally finding the questions quite easy, but I'm struggling to see what is wanted from me for this question. I'll give it a miss unless anyone knows better...