Question

if the sum of squares of two concecutive odd natural number is 290 .what are the numbers

Answer 1

Let the first no. Be a
Second No. = a +2

According to question

=> a^2 + (a+2)^2 = 290

=> a^2 + a^2 + 4a + 4 = 290

=> 2a^2 + 4a - 286 = 0

=> a^2 + 2a - 143 = 0

=> a^2 +13a - 11a - 143 = 0

=> a(a+13) - 11(a+13) = 0

=> (a+13)(a-11) = 0


a= 11 and - 13

Since a is a natural number
So,
a= 11

First no. = 11

Second No. = 13

Answer 2

Answer:

Step-by-step explanation:

Question:

If the sum of squares of two consecutive odd natural number is 290. What are the numbers ?

Solution:

This question says the sum of squares of two consecutive odd number is 290

Let the first no: be 'x'

Second no: is 'x + 2'

→ x² + (x + 2)² = 290

→ x² + x² + 4x + 4 = 290

→ 2x² + 4x + 4 - 290 = 0

→ 2x² + 4x - 286 = 0

→ 2(x² + 2x - 143) = 0

→ x² + 2x - 143 = 0

Take a look at this picture and you will see how the quadratic equation was solved

Final answer:

Therefore the numbers are x & 'x+2'

i.e. 11 & 13

Verification:

(11)² + (13)² = 290