Question

Heya...


Find x

$\sqrt{2x - 6} + \sqrt{x + 4} = 5$

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$<marquee > prabhudutt$
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Answer 1

√( 2x+6) + √( x+4) = 5

√( 2x + 6) = 5 - √( x+4)

squaring

2x +6 = 25 + x+ 4 - 10√(x+4)

2x + 6 - 25 - x -4 = -10√(x+4)

x -23 = -10√(x+4)

Again squaring

( x-23)^2 = 100( x+4)

x^2 + 529 - 46x -100x -400= 0

x^2 - 146x + 129= 0

x= 146 +-√(146)^2 -4(129))/2

= 146 +-√(21316 - 516))/2

= 146+-√1620))/2

= 146+-18√5))/2

= 73+- 9√5

x= 73 + 9√5

or 73 - 9√5