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3 years ago

The sum of two numbers is 51 and the difference is 13. what are the numbers

Mathematics

2 answers:

morpeh [17]3 years ago

8 0

Answer:

the two numbers are 19 and 32

Step-by-step explanation:

let's call the numbers x and y.

write out the equations

x + y = 51

x - y = 13

simplify the second equation

x = 13 + y

substitute into the first equation and simplify

(13 + y) + y = 51

13 + 2y = 51

2y = 51 - 13

2y = 38

y = 19

substitute y for 19 in the second equation

x = 13 + y

x = 13 + 19

x = 32

mylen [45]3 years ago

4 0

Answer:

Step-by-step explanation:

19 and 32

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1) Determine the discriminant of the 2nd degree equation below:

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$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

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$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

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So here,

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So here,

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So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

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