Solve x-6 = (x-4)^(1/2) and find any extraneous solutions

Lorelei Johnston

Lorelei Johnston

Answered question

2023-03-23

Solve x - 6 = ( x - 4 ) 1 2 and find any extraneous solutions

Answer & Explanation

pagarec0pz

pagarec0pz

Beginner2023-03-24Added 3 answers

x - 6 = ( x - 4 ) 1 2
( x - 6 ) 2 = x - 4
x 2 - 13 x + 40 = 0
0 = ( x - 13 2 ) 2 + 40 - 169 4
0 = ( x - 13 2 ) 2 - 9 4
x = 13 2 ± 9 4
x = 8; 5
momnatishai2hs

momnatishai2hs

Beginner2023-03-25Added 5 answers

( x - 6 ) 2 = ( ( x - 4 ) 1 2 ) 2
x 2 - 12 x + 36 = x - 4
x 2 - 13 x + 40 = 0
8 and 5 will work : 8 × 5 = 40 and 8 + 5 = 13
( x - 5 ) ( x - 8 ) = 0
letting each factor equal 0 gives x = 5 or x = 8

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