Question

solve the quadratic equations : solve the quadratic equations : the difference between two natural number is 4 the sum of their squares is 170. find the numbers.​ (don't use two variable)​

Answer 1

Step-by-step explanation:

Let,one number be 'x'.

second number=x+4

sum of their squares=170

${x}^{2} + {(x + 4)}^{2} = 170$

${x}^{2} + {x}^{2} + 16 + 8x$

$2 {x}^{2} + 8x + 16$

$2( {x}^{2} + 4x + 8) = 0$

${x}^{2} + 4x + 8 = 0$

X2 – 4x – 8 = 0

x2 – 4x = 8

x2 – 4x + 4 = 8 + 4

x2 – 4x + 4 = 12

(x – 2)2 = 12

Now I can square-root both sides of the equation, simplify, and solve:

Then the solution is

x=2+2√3

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