Question

Given that ormula1" title="\frac{8-3\sqrt{2} }{2} = a+b\sqrt{2}" alt="\frac{8-3\sqrt{2} }{2} = a+b\sqrt{2}" align="absmiddle" class="latex-formula">
Find a and b

Answer 1

Answer:

a = 4, b = - $\frac{3}{2}$

Step-by-step explanation:

Given

$\frac{8-3\sqrt{2} }{2}$ = a + b$\sqrt{2}$ ( multiply both sides by 2 to clear the fraction )

8 - 3$\sqrt{2}$ = 2a + 2b$\sqrt{2}$

For the 2 sides to be equal , then

2a = 8 ( divide both sides by 2 )

a = 4

and

2b = - 3 ( divide both sides by - 2 )

b = - $\frac{3}{2}$