Equations

Step 1: Given,

2f(x)-3f%5C!%5Cleft(%5Cfrac%7B1%7D%7Bx%7D%5Cright)%3Dx%5E2%20%5Cqquad%20(1)

Replace

x

%5Cdfrac%7B1%7D%7Bx%7D

2f%5C!%5Cleft(%5Cfrac%7B1%7D%7Bx%7D%5Cright)-3f(x)%3D%5Cfrac%7B1%7D%7Bx%5E2%7D%20%5Cqquad%20(2)

Step 2: Write equations (1) and (2) in standard form:

2f(x)-3f%5C!%5Cleft(%5Cfrac%7B1%7D%7Bx%7D%5Cright)%3Dx%5E2

-3f(x)%2B2f%5C!%5Cleft(%5Cfrac%7B1%7D%7Bx%7D%5Cright)%3D%5Cfrac%7B1%7D%7Bx%5E2%7D

Step 3: Multiply equation (1) by

2

and equation (2) by

3

4f(x)-6f%5C!%5Cleft(%5Cfrac%7B1%7D%7Bx%7D%5Cright)%3D2x%5E2

-9f(x)%2B6f%5C!%5Cleft(%5Cfrac%7B1%7D%7Bx%7D%5Cright)%3D%5Cfrac%7B3%7D%7Bx%5E2%7D

Step 4: Add the above equations:

-5f(x)%3D2x%5E2%2B%5Cfrac%7B3%7D%7Bx%5E2%7D

f(x)%3D-%5Cfrac%7B2x%5E2%2B%5Cfrac%7B3%7D%7Bx%5E2%7D%7D%7B5%7D

Step 5: Substitute

x%3D2

f(2)%3D-%5Cfrac%7B2(2)%5E2%2B%5Cfrac%7B3%7D%7B(2)%5E2%7D%7D%7B5%7D%0A%3D-%5Cfrac%7B8%2B%5Cfrac%7B3%7D%7B4%7D%7D%7B5%7D%0A%3D-%5Cfrac%7B%5Cfrac%7B35%7D%7B4%7D%7D%7B5%7D%0A%3D-%5Cfrac%7B7%7D%7B4%7D

Step 1: Let $t%3D%5Csqrt%7Bx%7D$ , where $t%5Cge%200$ . The given equation becomes: $2%7Ct-3%7C%2Bt(t-6)%2B6%3D0$
Step 2: Simplify the polynomial part: $t(t-6)%2B6%3Dt%5E2-6t%2B6$ So, $2%7Ct-3%7C%2Bt%5E2-6t%2B6%3D0$
Step 3: Consider cases due to the absolute value. Case I: $t%5Cge%203%20%5CRightarrow%20%7Ct-3%7C%3Dt-3$ $2(t-3)%2Bt%5E2-6t%2B6%3D0$ $t%5E2-4t%3D0$ $t(t-4)%3D0$ Valid solution (since $t%5Cge%203$ ): $t%3D4$ Case II: $0%5Cle%20t%3C3%20%5CRightarrow%20%7Ct-3%7C%3D3-t$ $2(3-t)%2Bt%5E2-6t%2B6%3D0$ $t%5E2-8t%2B12%3D0$ $(t-2)(t-6)%3D0$ Valid solution (since $t%3C3$ ): $t%3D2$
Step 4: Convert back to $x$ : $x%3Dt%5E2%20%5CRightarrow%20x%3D16%2C%5C%3B4$
Step 5: Hence, $S%3D%5C%7B4%2C16%5C%7D$ which contains exactly two elements.

About Equations - LPUNEST

Equations is a vital chapter for LPUNEST aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Equations PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Equations carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

About Equations - LPUNEST

Frequently Asked Questions

Why focus on Equations PYQs?

How to best use this analysis?

Equations

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

About Equations - LPUNEST

Frequently Asked Questions

Why focus on Equations PYQs?

How to best use this analysis?

Chapter Questions
2 MCQs