Question

The product of two consecutive integer were 2070. Find the integer.​

Answer 1

$\underline{\underline {\sf{\maltese \: \: To \: Find}}}$:

• Find the integers.

$\underline{\underline {\sf{\maltese \: \: Given}}}$:

• The product of two consecutive integers is 2070.

$\underline{\underline {\sf{\maltese \: \: Solution}}}$:

Let the first number be " x "

Second number be " x + 1 "

So,

$\tt\implies \: ( x ) ( x + 1 ) = 2070$

$\tt\implies \: {x}^{2} + x = 2070$

$\tt\implies \: {x}^{2} + x - 2070 = 0$

$\tt\implies \: {x}^{2} - 45x + 46x - 2070 = 0$

$\tt\implies \: x( x - 45 ) + 46( x - 45 ) = 0$

$\tt\implies \: ( x + 46 ) ( x - 45 ) = 0$

$\tt\implies \: x + 46 = 0 ; x - 45 = 0$

$\tt\implies \: x = - 46 \: ; \: 45$

Answer 2

Answer:

$\huge\bf\red{Answer:}$

$\bf\green{given}$

• product of two consecutive integers is 2070

$\bf\green{to\:find}$

• the two integers = ?

$\bf\green{assume:}$

• let the first integer be x
• let the second integer be x+1

Therefore by the given condition,

➡️ x × ( x + 1 ) = 2070

➡️ x² + x = 2070

➡️ x² + x - 2070 = 0

➡️ x² - 45x + 46x - 2070 = 0

➡️ x ( x - 45 ) + 46 ( x - 45 ) = 0

➡️ (x + 46) (x-45) = 0

➡️ x + 46 = 0; x - 45 = 0

➡️ x = -46 ; 45