Question

Find two numbers whose sum is 27 and product is 182 please help class 10 maths

Answer 1

Your Answer:

Given:-

• Sum of numbers = 27
• Product of numbers = 182

To Find:-

• The numbers

Solution:-

Let the numbers be x and y

ATQ,

$\tt x + y = 27 \rightarrow \rightarrow\rightarrow \rightarrow(1)$

and

$\tt x y = 182\rightarrow \rightarrow\rightarrow \rightarrow(2)$

From eq.(1)

$\tt x = 27 - y \rightarrow \rightarrow \rightarrow \rightarrow (3)$

Putting value of x from eq(1) into eq(2)

$\tt (27-y)y = 182 \\\\ \tt \Rightarrow 27y - y^2 = 182 \\\\ Multiplying \ \ with \ \ (-1) \ \ both \ \ sides \\\\ \tt \Rightarrow y^2 -27y = -182 \\\\ \tt \Rightarrow y^2 - 27y +182 = 0 \\\\ \tt \Rightarrow y^2 - 13y - 14y +182 = 0 \\\\ \tt \Rightarrow y(y-13) - 14(y -13) = 0 \\\\ \tt \Rightarrow (y-14)(y-13) = 0 \\\\ \tt Equating \ \ the \ \ factors \ \ with \ \ zero$

$\tt \star First \ \ Equating \ \ (y-14) \ \ with \ \ 0 \\\\ y - 14 = 0 \\\\ \tt \Rightarrow y =14 \\\\ \tt \star Second \ \ Equating \ \ (y-13) \ \ with \ \ 0 \\\\ y - 13 = 0 \\\\ \tt \Rightarrow y =13$

So, for the first case y = 14

then x = 13

And for the second case y = 13

then x = 14

So, the numbers are 13 and 14

Answer 2

Let the two numbers be x and y.

Given

Sum of the 2 numbers is 27

$\implies x+y=27\\\implies x = 27-y--(1)$

Product of the two numbers is 182

$\implies xy=182$

$\implies y(27-y)=182$

$\implies -y^{2} +27y=182\\\implies y^{2} -27y+182=0\\\implies y^{2}-14y-13y+182=0\\\implies y(y-14)-13(y-14)=0\\\implies (y-14)(y-13)=0$

If y = 14, x = 13

If x = 13, y = 14

$\boxed{\boxed{\bold{Therefore, \ the \ numbers \ are \ 13 \ and \ 14}}}}}}}}}$