Question

5 If an integer is added to its square, the
is 90. Find the integer with the help
of quadralic equation
suma​

Answer 1

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

x = -10 , x = 9

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

If an integer is added to its square, the

sum is 90.

$\sf\underline{\red{\:\:\: To\: Find:-\:\:\:}}$

Integer with the help of quadratic equation

$\sf\underline{\red{\:\:\: Solution:-\:\:\:}}$

Let the integer = x.

So, the square of the integer = x².

$\sf\underline{\red{\:\:\: According\: to\: question\:\:\:}}$

$\leadsto$ x² + x = 90

$\leadsto$ x² + x -90 = 0

$\leadsto$ x² + 10x - 9x - 90 = 0

$\leadsto$ x( x + 10 ) -9( x + 10 ) = 0

$\leadsto$ ( x + 10 )( x - 9 ) = 0

$\leadsto$ x = -10 or x = 9

Hence, x = -10 and x = 9 are required values of x.

Answer 2

$\huge\sf\red{Correct \: Question :}$

If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.

$\Huge\bf\pink{⛧Solution:}$

Let the required integer be x.

Then according to the given condition

⇒ x + x2 = 90

⇒ x2 + x – 90 = 0

⇒ x2 + 10x – 9x – 90 = 0

⇒ x(x + 10) – 9(x + 10) = 0

⇒ (x + 10)(x – 9) = 0

⇒ x + 10 = 0 or x – 9 = 0

$<font color=pink>$

⇒ x = - 10 or x = 9

$<font color=green>$

Hence, the required integer is - 10 or 9 .