Question

solve: sqrt(4x+9)+sqrt(4x-9)=5+sqrt(7)`​

Answer 1

Answer:

Step-by-step explanation:

√4x-9+√4x+9=5+√7

=√4x+√4x=5+√7

simplyfy the radical

2√x+√4x=5+√7

calculate the square root

2√x+2x=5+√7

Move variable to right side and change it's sign

2√x+5+√7-2x

square both sides of equation

4x=25+7+4x²+10√7-20x-4√7x

Add the no.

4x=32+4x²+10√7-20x-4√7x

Move the expression to the left side and change it's sign.

4x -32-4x²-10√7+20x+4√7x=0

Collect like terms

24x-32-4x²-10√7+√7=0

Factor out x from the equations

(24+4√7)x-32-4x²-10√7=0

use commutative property

-4x²+(24+4√7)x-32-10√7=0

solve the quadratic equation

x=-(25+4√7)_+_√(24+4√7)²-4×(-4)×(-32-10√7)/2×(-4)

x=-(24+4√7)_+_√(24+4√7)²+4×4(-32-10√7)/2×(-4)

Determine the sign of the fraction

x=-(24+4√7)_+_√(24+4√7)²+4×4(-32-10√7)/2×4

x=-24-4√7_+_√576+192√7+112+16(-32-10√7)/8

Distribute by 16

x=-24-4√7_+_√576+192√7+112-512-160√7/8

x=-24-4√7_+_√176+32√7/8

simplyfy the root

x=-24-4√7_+_2²×√11+2√7/8

Evaluate the power

x=-24-4√7+4√11+2√7/8

x=-24-4√7-4√11+2√7/8

simplyfy the expression

x=-6-√7_+_√11+2√7/2

x=-6-√7-√11+2√7/2

Final solution

x=-6-√7+√11+2√7/2

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