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valkas [14]
2 years ago
15

Solve. Check for extraneous solutions. √2 x+6 - √x-1 =2

Mathematics
1 answer:
Alex2 years ago
8 0

x = 5 is not an extraneous solution of the equation.

✓(2x + 6) - ✓(x - 1) = 2

✓(2x + 6) = 2 + ✓(x - 1)

Squaring both the sides of equation, we get

(✓(2x + 6))² = (2 + ✓(x - 1))²

2x + 6 = (2)² + (✓(x - 1))² + 2(2)(✓(x - 1))

2x + 6 = 4 + x - 1 + 4(✓(x - 1))

x + 3 = 4✓(x - 1)

Squaring again on both the side of the equation, we get

(x + 3)² = (4✓(x - 1))²

x² + 3² + 2×3×x = 16(x - 1)

x² + 9 + 6x = 16x - 16

x² - 10x + 25 = 0

By applying middle term splitting on equation (1), we get

x² - 5x - 5x + 25 = 0

x(x - 5) -5(x - 5) = 0

(x - 5) (x - 5) = 0

x = 5 and 5.

Check for extraneous solutions by putting value of x in original equation -

✓(2×5 + 6) - ✓(5 - 1) = 2

✓16 - ✓4 = 2

4 - 2 = 2

2 = 2

LHS = RHS

x = 5 is not an extraneous solution of the equation.

Know more about roots of equation -

brainly.com/question/4098861

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