Given that (√3-5√2)(√3+2)=a+b√6. Find a and b. Show workings bit by bit

Answer 1

First, we need to multiply (√3-5√2) by (√3+2). We can use the distributive property to do this:

(√3-5√2)(√3+2) = √3(√3+2) - 5√2(√3+2)

Next, we can simplify each term inside the brackets:

√3(√3+2) = (√3*√3) + (√3*2) = 3+2√3

-5√2(√3+2) = -5√2*√3 -5√2*2 = -5√6 -10√2

Now, we can combine the simplified terms:

(3+2√3) - (5√6 + 10√2)

Next, we can distribute the negative sign to each term inside the bracket:

3 + 2√3 - 5√6 - 10√2

Finally, we can rearrange the terms:

3 - 10√2 + 2√3 - 5√6

The final form is a+b√6, so we need to group like terms:

(3 - 10√2) + (2√3 - 5√6)

Therefore, a = 3 - 10√2 and b = 2√3 - 5√6.