Find two consecutive positive integers, sum of whose squares is 365 ?

byAmlesh Mahato •March 04, 2021

The Biotic World is the best free Educational Website for Students. The Biotic World Provides NCERT Solution PDF, CBSE Notes PDF, NCERT Books PDF for class 8, 9, 10, 11, 12. The Biotic World also provides GU TDC Syllabus, Previous Years Question Papers, TDC notes on different topics of Physics, Chemistry, Mathematics, Zoology and Botany any many more. So, Follow us to get tuned with latest updates.

Solution:

⇨ Let the two consecutive positive integers are x, x+1

A/Q

$Find two consecutive positive integers, sum of whose squares is 365.$

$\large \Rightarrow x^2+x^2+2x+1=365$

$\large \Rightarrow 2x^2+2x+1-365=0$

$\large \Rightarrow 2x^2+2x-364=0$

⇨Divided by 2 on both side

$\large \Rightarrow x^2+x-182=0$

$\large \Rightarrow x^2+(14-13)x-182=0$

$\large \Rightarrow x^2+14x-13x-182=0$

$\large \Rightarrow x(x+14)-13(x+14)=0$

$\large \Rightarrow (x-13)(x+14)=0$

$\large \Rightarrow x-13=0,x+14=0$

$\large \Rightarrow x=13,x=-14$

⇨x = -14, We only consider positive integers, so -14 is rejected.

⇨Therefore, Two consecutive positive integers are = x , x+1

⇨13 , 13+1

⇨13, 14

Exercise 4.2

1. Find the roots of the following quadratic equations by factorisation:

(i) $x^2-3x-10=0$

(ii) $Find the roots of 2x^2+x-6=0 quadratic equations by factorization ?$

(iii) $Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?$

(iv) $Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?$

(v) $\large 100x^{2}-20x+1=0$

3. Find two numbers whose sum is 27 and product is 182.

4. Find two consecutive positive integers, sum of whose squares is 365.

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ` 90, find the number of articles produced and the cost of each article.

Tags: Chapter-4 Exercise-4.2 Math- Class 10