Question

the square of a number is 60 more than 7 times the number find the number

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Question:

• The square of a number is 60 more than 7 times the number. find the number .

Solution:

Let the number be x.

As per question ,

The square of number( say x²) is 60 more than 7 times the number (say 60 + 7x ).

According to the question,

We got : x² = 60 + 7x

$\longmapsto x^2 -60 -7x =0$

Here we have got a quadratic equation so, now we can find the number by solving this equation.

$\longmapsto x^2 -7x-60 =0$

$\dashrightarrow x^2 -12x+5x-60=0 \\\\\dashrightarrow x(x-12)+5(x-12)=0$

$\dashrightarrow (x-12)(x+5)=0$

$\dashrightarrow \sf x-12=0 \quad or \quad x+5=0$

$\dashrightarrow x=12\; or\; x= -5$

$\dashrightarrow x=-5,12$

Therefore,

• The number can be -5 and 12.

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Verification:

$\bigstar\pink{\textbf{Putting x = -5}}$

x² -7x -60 = 0

-5² -7(-5) -60

25 + 35 -60

25 - 25

0

L.H.S = R.H.S

_____________

$\bigstar\pink{\textbf{Putting x = 12}}$

x² -7x -60 = 0

12² -7(12) -60

144 -84 -60

144 - 144

0

L.H.S = R.H.S

$\large\green{\underline{\mathfrak{Hence\;verified\displaystyle !\,}}}$