solve √ 4x - 3 + √ 2x + 3 = 6.
Answers
√(4x-3) +√(2x+3) = 6
Step 1 :
√(4x - 3) = - √(2x + 3) + 6
Step 2 :
Eliminate the radical on the left hand side :
(√4x-3)² = (-√(2x+3)+6)²
4x - 3 = 2x + 3 + 36 - 12√2x + 3
12√2x+3 = -4x+3+2x+3+36
12√2x+3 = -2x+42
Step 3 :
Eliminate the radical on the left hand side :
(12√2x+3)² = (-2x+42)²
288x+432 = 4x²-168x+1764
4x² - 456x + 1332 = 0
x = 111, 3
Now check the solutions are correct
Step 4 :
√(4x-3) = -√(2x+3)+6
x= 111
√[4*(111)- 3] = -√[2*(111)+3]+6
√(444- 3) = -√(222+ 3 )+ 6
√441 = -15 + 6
21 ≠ -9
So x = 111 will not work
Step 5 :
Check whether x=3 is correct
√4x-3 = -√2x+3+6
√4*(3)-3 = -√2*(3)+3+6
√9 = - 3 + 6
3 = 3
∴ x = 3
Answer:
Step-by-step explanation:
√4x-3 +√2x-3 =6
(√4x-3)^2={6-(√2x+3)}^2 (square on both sides)
4x-3 = 36+2x+3-12√2x+3(a^2+b^2-2ab=(a-b)^2)
4x-3-36-2x-3=(-12√2x+3)(rearranged )
2x-42= -12√2x+3
x-21 = -6√2x+3(divided on both sides by 2)
(x-21)^2 = (-6√2x+3)^2(square on both sides)
X^2+441-42x =36(2x+3)
x^2+441-42x-72x-108=0
x^2-114x+333=0
x^2-111x-3x+333=0(factorisation)
x(x-111)-3(x-111)=0
(x-111)(x-3)=0
x=111 or x=3
Accurate ans x=3