Question

Difference of 2 numbers is 2 and product of them is 224 find the numbers.

Answer 1

Answer:

-16 and -14 or 14 and 16

Step-by-step explanation:

let the number be x

then the other number will be x+2

ATQ,

x(x+2)=224

=>x²+2x=224

=>x²+2x-224=0

=>x²+16x-14x-224=0

=>x(x+16)-14(x+16)=0

=>(x+16)(x-14)=0

=>x+16=0 or x-14=0

=>x=-16 or x=14

Case I , if x=-16

then x+2=-16+2=-14

case II , if x=14

then x+2=14+2=16

so the pair of numbers are -16 and -14 or 14 and 16

Answer 2

Given:-

• The difference of two number is 2 and product of them is 224.

To Find:-

• The Numbers

Solution:-

$\begin{gathered}\begin{gathered} \sf \: Let \: the \: numbers \: be \: \pink{x \: and \: y} \\ \\ \purple{\bf \: x - y = 2 - - - (i)} \\ \\ \end{gathered}\end{gathered}$

Now to find the answer we have to find x + y

$\begin{gathered}\begin{gathered} \sf \: (x + y) ^{2} = (x - y) {}^{2} + 4xy \\ \looparrowright \sf \: {(x + y)}^{2} = ( {2)}^{2} + 4(224) \\ \looparrowright \sf \: {(x + y)}^{2} = 4 + 896 \\ \looparrowright \sf \: {(x + y)}^{2} = 900 \\ \looparrowright \sf \: x + y = \sqrt{900} \\ \looparrowright \bf \purple{\:x + y = 30} \\ \\ \end{gathered}\end{gathered}$

Now x + y = 30

x - y = 2

Adding (i) and (ii)

$\begin{gathered}\begin{gathered} \rm \: x + y = 30 \\ \rm \: x - y = 2 \\ - - - - - - \\ \rm \: 2x = 32 \\ \purple {\boxed {\bf x = 16}} \\ \\ \sf \: x + y = 30 \\ \sf \: 16 + y = 30 \\ \purple{ \boxed{ \bf \: y = 14}} \\ \\ \color{maroon} \boxed{\begin{array}{c} \: \sf \: x = 16 \\ \sf y = 14 \end{array}}\end{gathered}\end{gathered}$