Question

express sqrt of 4x^2-9 in the form k sqrt x^2-a^2

Answer 1

\[\large \sqrt{4x^2-9}\]



\[\large \sqrt{4(x^2-\frac{9}{4})}\]



\[\large \sqrt{4}\sqrt{x^2-\frac{9}{4}}\]



\[\large 2\sqrt{x^2-\frac{9}{4}}\]



\[\large 2\sqrt{x^2-(\frac{3}{2})^2}\]

So \[\large \sqrt{4x^2-9}=2\sqrt{x^2-(\frac{3}{2})^2}\]

Note: k=2 and a=3/2

Answer 2

thank you