Question

If f(x) =x²+5x+7,then the value of x for which f(x) =f(x+1) is​

Answer 1

Step-by-step explanation:

$f(x) = f(x + 1) \\ \\ {x}^{2} + 5x + 7 = {(x + 1)}^{2} + 5(x + 1) + 7 \\ \\ {x}^{2} + 5x = {x}^{2} + 2x + 1 + 5x + 5 \\ \\ 2x + 6 = 0 \\ \\ 2x = - 6 \\ \\ x = - 3$

Answer 2

The x value is -3

Given:

f(x) =x²+5x+7

And given condition f(x) = f(x+1)

To find:

The value of x

Solution:

Given that f(x) = x²+5x+7  

And f(x) =f(x+1)

Here to find f(x+1) substitute (x+1) instead of x in f(x)

⇒ f(x+1) = (x+1)²+5(x+1)+7  

= x²+ 1 +2x +5x + 5 + 7  

= x²+ 1 +7x + 5 + 7  

= x² +7x + 13

By given condition f(x) = f(x+1)

⇒ x² + 5x + 7 = x² +7x + 13

⇒ x² - x² + 5x -7x = 13 - 7

⇒  -2x = 6

⇒ x = 6/-2 = -3

⇒  x = -3

Therefore, the x value is -3

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