17 find all real solutions Find all real solutions square ro

17. find all real solutions.

Find all real solutions. square root 2 w + 1 = square root 4 - w

given

-3 + sqrt (2w +1) = sqrt (4 -w)

squaring on both sides

[ -3 + sqrt (2w +1) ]^2 = [sqrt(4-w) ]^2

(-3)^2 + ( sqrt (2w +1))^2 + 2(-3)sqrt (2w +1) = 4-w

9 + 2w+1 -6sqrt(2w+1) = 4-w

-6sqrt(2w+1) = 4 -w -2w -10

-6sqrt(2w+1) = -6-3w

againg squaring on both sides

[-6sqrt(2w+1) ]^2 = (-6-3w)^2

36(2w+1) = 36 +9w^2 +36w

72w +36 = 9w^2 +36w +36

9w^2 -36w =0

9w(w-4) =0

so this will be true

when w = 0 or w-4 =0

but w=0 doesn\'t satisfy the given condition

so w=4 is the answer