Question

n square + n = 72 what is the value of n​

Answer 1

Answer:

$\large{\underline{\boxed{\sf n = 8}}}$

Step-by-step explanation:

Given that ;

n² + n = 72

⇒ n² + n - 72 = 0

We can solve this question by splitting the middle term. We need two numbers such that the product of numbers is (-72) and sum of the numbers is 1.

Two numbers can be 9 and (-8).

⇒ n² + n - 72 = 0

On splitting the middle term ;

⇒ n² + 9n - 8n - 72 = 0

⇒ n(n + 9) - 8(n + 9) = 0

⇒ (n + 9)(n - 8) = 0

By zero product rule ;

⇒ n = - 9 or n = 8

Thus, taking the positive value.

∴ The value of n is 8.

Answer 2

Hi there !!

${n}^{2} + n \: = 72 \\ \\ {n}^{2} + n - 72 = 0$

Spitting the middle term by factorisation method.

${n}^{2} + 9n - 8n - 72 = 0 \\ \\ n(n + 9) - 8(n + 9) \\ \\ n + 9 = 0 \\ \\ n - 8 = 0$

Hence,

n= -9 and 8

Ignoring negative value..

n= 8

Thank you :)