Question

the product of two consecutive integers is 30 what are the numbers

Answer 1

Step-by-step explanation:

let the two consecutive integer be x and x+1

Product will be

${x}^{2} + x = 30 \\ {x }^{2} + x - 30 = 0 \\ {x}^{2} - 5x + 6x - 30 = 0 \\ x(x - 5) + 6(x - 5) = 0 \\ x - 5 = 0 \: and \: x + 6 = 0 \\ x = 5 \: and \: x = - 6$

since, it is given integer, so it can be either 5 or -6.

Answer 2

Given :- The product of two consecutive integers is 30 what are the numbers ?

Answer :-

Let us assume that, the first integer is x .

so,

→ second integer = (x + 1) .

then,

→ first integer * second integer = 30

→ x * (x + 1) = 30

→ x² + x = 30

→ x² + x - 30 = 0

→ x² + 6x - 5x - 30 = 0

→ x(x + 6) - 5(x + 6) = 0

→ (x + 6)(x - 5) = 0

→ x = (-6) and 5 .

therefore,

• when first number is (-6), second number will be (-5) .
• when first number is 5, second number will be 6 .

Hence, the numbers are (-6, - 5) or (5, 6) .

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