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The sum of the squares of two consecutiv...

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

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The correct Answer is:
15 and 17
`x^(2)+(x+2)^(2)=514implies2x^(2)+4x-510=0impliesx^(2)+2x-255=0`
`impliesx^(2)+17x-15x-255=0.`
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RS AGGARWAL-QUADRATIC EQUATIONS -Exercise 4E
  1. The sum of two natural number is 28 and their product in 192. Find the...

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

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  3. The sum of the squares of two consecutive positive odd numbers is 514....

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  4. The sum of the squares of two consecutive positive even numbers is 452...

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  5. The product of two consecutive positive integers is 306. Form the q...

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  6. Two numbers differ by 3 and their product is 504. Find the number.

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  7. Find two consecutive multiples of 3 whose product is 648.

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  8. The product of two consecutive odd numbers in 483. Find the numbers.

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  9. Find two consecutive positive even integers whose product is 288.

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  10. The sum of two natural numbers is 9 and the sum of their reciprocals i...

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  11. The sum of two numbers a and b is 15, and the sum of reciprocal of num...

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  12. The difference of two natural numbers is 3 and the difference of th...

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  13. The difference of two natural numbers is 5 and the difference of their...

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  14. The sum of the squares of two consecutive multiples of 7 is 1225. Find...

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  15. The sum of a natural number and its reciprocal is (65)/(8). Find the n...

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  16. Divide 57 into two parts whose product is 680.

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  17. Divide 27 into two parts such that the sum of their reciprocals is 3/2...

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  18. Divide 16 into two parts such that twice the square of the larger p...

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  19. Find two natural numbers, the sum of whose squares is 25 times their s...

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  20. The difference of the squares of two numbers is 45. The square of the ...

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