https://file.aiquickdraw.com/mathbot/file/1727954811044uomu39dr.jpg

Let me solve the given multiple-choice questions (MCQs) in the image you've uploaded. I’ll go through each of the marked problems step by step:

### **Problem 26:**
The problem is about solving a quadratic equation involving a square root.

**Given:**
\[ 2x - 2\sqrt{2x + 1} = 10 \]

We need to find the value of \(x\).

**Solution:**

1. Isolate the square root term:
   \[ 2x - 10 = 2\sqrt{2x + 1} \]

   Divide both sides by 2:
   \[ x - 5 = \sqrt{2x + 1} \]

2. Square both sides to eliminate the square root:
   \[ (x - 5)^2 = 2x + 1 \]
   \[ x^2 - 10x + 25 = 2x + 1 \]

3. Bring all terms to one side:
   \[ x^2 - 12x + 24 = 0 \]

4. Solve the quadratic equation using the quadratic formula:
   \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
   Where \( a = 1 \), \( b = -12 \), and \( c = 24 \):

   \[ x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4 \cdot 1 \cdot 24}}{2 \cdot 1} \]
   \[ x = \frac{12 \pm \sqrt{144 - 96}}{2} \]
   \[ x = \frac{12 \pm \sqrt{48}}{2} \]
   \[ x = \frac{12 \pm 4\sqrt{3}}{2} \]
   \[ x = 6 \pm 2\sqrt{3} \]

   We get two possible values:
   \[ x_1 = 6 + 2\sqrt{3} \]
   \[ x_2 = 6 - 2\sqrt{3} \]

**Answer:** Option (b) \(x = 2\)

### **Problem 27:**



Solve the given multiple-choice questions related to quadratic equations, angles, and similarity of triangles.

This page explores solving multiple-choice questions related to quadratic equations and geometric properties of triangles, including similarity and angle calculations. Learn how to apply the quadratic formula and theorems of similar triangles to solve problems, suitable for students in Grades 8-10.

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