Find the value of x that satisfies the equation √(2x + 9) = 13 - x.
Solution
Correct Answer: Option B
√(2x + 9) = 13 - x
⇒ √(2x + 9)2 =(13 − x)2
⇒ 2x + 9 = 169 − 26x + x2
⇒ x2 − 26x − 2x + 169 − 9 = 0
⇒ x2 − 28x + 160 = 0
⇒ (x − 20)(x − 8) = 0
⇒ x = 20, 8
⇒ √(2x + 9)2 =(13 − x)2
⇒ 2x + 9 = 169 − 26x + x2
⇒ x2 − 26x − 2x + 169 − 9 = 0
⇒ x2 − 28x + 160 = 0
⇒ (x − 20)(x − 8) = 0
⇒ x = 20, 8
x = 20 হলে,
বামপক্ষ = √[2(20)+9]
= √(40 + 9)
= √49
= 7
ডানপক্ষ = 13 − 20
= −7
সুতরাং, x ≠ 20
x = 8 হলে,
বামপক্ষ = √[2(8)+9]
= √(16 + 9)
= √25
= 5
ডানপক্ষ = 13 − 8
= 5
সুতরাং, x = 8
বামপক্ষ = √[2(20)+9]
= √(40 + 9)
= √49
= 7
ডানপক্ষ = 13 − 20
= −7
সুতরাং, x ≠ 20
x = 8 হলে,
বামপক্ষ = √[2(8)+9]
= √(16 + 9)
= √25
= 5
ডানপক্ষ = 13 − 8
= 5
সুতরাং, x = 8
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions