Question

SOMEONE HELP ME IM FREAKING OUT I LITERALLY CANT WITH THIS QUESTION IM PRAYING PLEASE HELP ME IM SO SERIOUS IM GONNA END IT PLS HELP ME the question is like 3-v BUT LIKE THE v has a line on top so its like 3-v32/1+v2 LIKE I DONT UNDERSTAND

can be written in the form a + bv2
where a and b are integers .

Answer 1

`\sf -11+7√(2)`

Explanation:

Given expression:

`\sf (3-√(32))/(1+√(2) )`

Rewrite 32 as 16 · 2:

`\sf \implies (3-√(16 \cdot 2))/(1+√(2) )`

Apply radical rule
`\sf √(a \cdot b)=√(a)√(b)`

`\sf \implies (3-√(16)√(2))/(1+√(2) )`

As
`\sf √(16)=4`:

`\sf \implies (3-4√(2))/(1+√(2) )`

Multiply by the conjugate:

`\sf \implies (3-4√(2))/(1+√(2) ) * (1-√(2) )/(1-√(2) )`

`\sf \implies ((3-4√(2))(1-√(2)))/((1+√(2))(1-√(2)))`

`\sf \implies (3-3√(2)-4√(2)+4√(2)√(2))/(1-√(2)+√(2)-√(2)√(2))`

As
`\sf √(2)√(2)=√(4)=2`:

`\sf \implies (3-3√(2)-4√(2)+4 \cdot 2)/(1-√(2)+√(2)-2)`

`\sf \implies (3-7√(2)+8)/(1-2)`

`\sf \implies (11-7√(2))/(-1)`

`\sf \implies -11+7√(2)`