Question

The product of two successive numbers is 4692. which is the smaller of the two

Answer 1

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Answer 2

Answer:

Required smaller number is -69 or 68.

Step-by-step explanation:

Given,The product of two successive numbers is 4692.

Let two numbers be x and (x+1)

According to question,

$x \times (x + 1) = 4692 \\ {x}^{2} + x - 4692 = 0 \\ {x}^{2} + (69 - 68)x - 4692 = 0 \\ {x}^{2} + 69x - 68x - 4692 = 0 \\ x(x + 69) - 68(x + 69) = 0 \\ (x + 69)(x - 68) = 0 \\ (x + 69) = 0 \: or \: (x - 68) = 0\\ x = - 69 \: or \: 68$

So, numbers are -69 and -68 or 68 and 69.

Therefore, required smaller number is (-69) or 68.

This is a problem of Algebra.

Some important Algebra's formula:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Two more important Algebra problem:

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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