MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 32(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerQuadratic Equations

Find two consecutive odd integers, sum of whose squares is 290.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Consecutive odd integers differ by 2, so take them as x and x + 2.

Hint 2

Form the equation from the sum of squares, simplify, and factorise; look for two numbers with product −143 and sum 2.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Let the two consecutive odd integers be $x$ and $x + 2$ .
½ mark
According to the question: $x^{2} + (x + 2)^{2} = 290$
1½ marks
$x^{2} + x^{2} + 4 x + 4 = 290 \Rightarrow 2 x^{2} + 4 x - 286 = 0 \Rightarrow x^{2} + 2 x - 143 = 0$
1½ marks
$x^{2} + 13 x - 11 x - 143 = 0 \Rightarrow (x - 11) (x + 13) = 0 \Rightarrow x = 11$ or $x = - 13$
1 mark
The required integers are 11 and 13. Check: $121 + 169 = 290$ . (The root $x = - 13$ gives the pair $- 13, - 11$ , which also works.)
½ mark

Answer: 11 and 13 (also −13 and −11)

Where the marks are

Takes the integers as x and x + 2 (½ mark)
Forms $x^{2} + (x + 2)^{2} = 290$ (1½ marks)
Simplifies to $x^{2} + 2 x - 143 = 0$ (1½ marks)
Solves to get x = 11 (1 mark)
States the integers 11 and 13 (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Word Problems on Quadratic Equations

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/3/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2025: question 32(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Quadratic Equations