The sum of the squares of two consecutive positive integers is 841. If larger number is x, then the algebraic representation will be.b
Answers
Step-by-step explanation:
Solution:
Let the two consecutive two natural numbers be (x) and (x +1) respectively.
Given,
That the sum of their squares is 85.
Then, by hypothesis, we get, = x2 + (x + 1)2 = 85
= x2 + x2 + 2x + 1 = 85
= 2x2 + 2x + 1 - 85 = 0
= 2x2 + 2x + - 84 = 0
= 2(x2 + x + -42) = 0
Now applying factorization method, we get, = x2 + 7x - 6x - 42 = 0
= x(x + 7) - 6(x + 7) = 0
= (x - 6)(x + 7) = 0
Either, x - 6 = 0 therefore, x = 6 x + 7 = 0 therefore x = -7
Hence the consecutive numbers whose sum of squares is 85 are 6 and -7 respectively.
Question: 2
Divide 29 into two parts so that the sum of the squares of the parts is 425.
Solution:
Let the two parts be (x) and (29 - x) respectively.
According to the question, the sum of the two parts is 425.
Then by hypothesis, = x2 + (29 - x)2 = 425
= x2 + x2 + 841 + -58x = 425
= 2x2 - 58x + 841 - 425 = 0
= 2x2 - 58x + 416 = 0
= x2 - 29x + 208 = 0
Now, applying the factorization method = x2 - 13x - 16x + 208 = 0
= x(x - 13) - 16(x - 13) = 0
= (x - 13)(x - 16) = 0
Either x - 13 = 0 therefore x = 13 Or, x - 16 = 0 therefore x = 16
The two parts whose sum of the squares is 425 are 13 and 16 respectively.
Answer:
x² + x - 420 = 0
Step-by-step explanation:
The sum of the squares of two consecutive positive integers is 841.
Assume that the numbers are (x) and (x + 1) respectively.
As said in question, sum and square of those numbers is 841. i.e.
→ (x)² + (x + 1)² = 841
Used identity: (a + b)² = a² + b² + 2ab
→ x² + x² + 1 + 2x = 841
→ 2x² + 2x = 841 - 1
→ 2x² + 2x = 840
Take 2 as common,
→ 2(x² + x ) = 2(420)
→ x² + x = 420
→ x² + x - 420 = 0
Hence, the algebraic representation of the situation is x² + x - 420 = 0.