Question

If √(x + 5) +√(5 - x) = 4. then, x = ?​

Answer 1

Answer:

x=±√7

Step-by-step explanation:

√(x+5) + √(5-x) = 4

Squaring Both Sides

x+5 + 5-x + √(2(5+x)(5-x)) = 16

√2(25-x²) = 16-10

Squaring Both Sides

2(25-x²) = 36

25-x² = 18

x² = 7

x = ±√7

Answer 2

$\sqrt{(x + 5)} + \sqrt{(5 - x)} = 4 \\ ( {x + 5)}^{2} + (5 - x) ^{2} = 4$

Using the identities:

$(x + y)^{2} = x^{2} + y^{2} + 2xy \\ (x - y)^{2} = x^{2} - 2xy + y ^{2}$

therefore,

$x ^{2} + 2(x)(5) + 5^{2} + {5}^{2} - 2(5)(x) + {x}^{2} = 4 \\ {x}^{2} + 10x + 25 + 25 - 10x + {x}^{2} = 4 \\ {2x}^{2} + 50 = 4 \\ {2x}^{2} = 4 - 50 \\ {2x}^{2} = - 46$

${x}^{2} = 2 \div - 46 \\ {x}^{2} = - 23 \\ x = \sqrt{ - 23}$