PREVIOUSLY ASKED IN:
CTET 2026
Answer
\( 2\frac{4}{5} \)
Explanation
Using the algebraic identity, \( (a+b)^2 = (a-b)^2 + 4ab \). Substituting the values, we get \( (a+b)^2 = (\frac{11}{5})^2 + 4(\frac{3}{4}) = \frac{121}{25} + 3 = \frac{121 + 75}{25} = \frac{196}{25} \). Taking the square root, \( (a+b) = \frac{14}{5} \). In mixed fraction format, this is equal to \( 2\frac{4}{5} \).
Key Points
- > Such problems rely heavily on algebraic identities of squares.
- > The formula \( (a+b)^2 = (a-b)^2 + 4ab \) is a crucial identity.
- > When \( (a-b) \) and \( ab \) are given, using this formula provides a direct solution.
- > Usually, the positive square root is considered unless options suggest otherwise.
- > Properly calculate the LCM when adding or subtracting fractions.
- > Remembering perfect squares like \( 196 = 14^2 \) and \( 25 = 5^2 \) speeds up calculation.
- > Converting improper fractions to mixed fractions is essential for matching options.
Additional Information
Important Algebraic Identities
| Formula | Expanded Form | Use Case |
|---|---|---|
| (a+b)² | a² + b² + 2ab | Square of sum |
| (a-b)² | a² + b² - 2ab | Square of difference |
| (a+b)² - (a-b)² | 4ab | Finding product (ab) |
| (a+b)² + (a-b)² | 2(a² + b²) | Finding sum of squares |
Memory Tips
- Key Difference: When converting between (a+b) and (a-b), always use the 4ab identity, not 2ab.
- Fraction Trick: Practice finding the LCM of denominators quickly to avoid calculation errors.