CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Let Us Find Two Natural Numbers Which Differ by 3 and Whose Squares Have the Sum 117. - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

Let us find two natural numbers which differ by 3 and whose squares have the sum 117.

Solution

Let the numbers be x and x - 3

By the given hypothesis,

𝑥2 + (𝑥 - 3)2 = 117

⇒ 𝑥2 + 𝑥2 + 9 - 6𝑥 - 117 = 0

⇒ 2𝑥2 - 6𝑥 - 108 = 0

⇒ 𝑥2 - 3𝑥 - 54 = 0

⇒ 𝑥(𝑥 - 9) + 6(𝑥 - 9) = 0

⇒ (x - 9) (x + 6) = 0

⇒ x = 9 or x = -6

Considering positive value of x

x = 9, x - 3 = 9 - 3 = 6

∴ The two numbers be 9 and 6.

  Is there an error in this question or solution?

APPEARS IN

Solution Let Us Find Two Natural Numbers Which Differ by 3 and Whose Squares Have the Sum 117. Concept: Solutions of Quadratic Equations by Factorization.
S
View in app×