Question

1) The difference of two number is 2 and product of them is 224.Find the Numbers.

Answer 1

Answer:

x = 16

y = 14

Step-by-step explanation:

Given:-

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

To Find:-

• The Numbers

Solution:-

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

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

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

Now x + y = 30

x - y = 2

Adding (i) and (ii)

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