Answer :
Answer:
To find the number of real values of x satisfying the equation, you can start by simplifying it:
x² + x + √(x² + x + 7) = 5
Subtract x² + x from both sides:
√(x² + x + 7) = 5 - x² - x
Square both sides of the equation:
x² + x + 7 = 25 - 10x² - 10x + x⁴ + 2x³ + x²
Simplify the right side:
x⁴ + 2x³ - 9x² - 11x + 18 = 0
This is a quartic equation. Solving quartic equations can be quite involved, often requiring numerical methods. However, you can analyze the polynomial to determine the number of real roots.
Since it’s a quartic equation, it can have a maximum of 4 real roots. The correct answer is (D)4.
Thank you
Explanation:
∣
x
3
x
+
2
2
x
−
1
2
x
−
1
4
x
3
x
+
1
7
x
−
2
17
x
+
6
12
x
−
1
∣
∣
∣
∣
=
0
Applying
R
3
→
R
3
−
3
R
1
−
2
R
2
we get