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Find the two consecutive numbers whose squares have the sum 85 by quadratic equation formula)

Answers (1)
D Deependra Verma

Let the number $$x$$\$$

and its consecutive number $$ = x + 1 $$\$$

According to the question, 

                              $$ x ^2 + (x + 1)^2 = 85 $$\$$ $$Rightarrow x^2 + x^2 + 1 + 2x = 85$$\$$ $$Rightarrow 2x^2 + 2x -84 = 0 $$\$$ $$Rightarrow x^2 + x - 42 = 0 $$\$$ $$Rightarrow x^2 + 7x - 6x - 42 = 0 $$\$$ $$Rightarrow(x -6) (x+7) = 0 $$\$$ $$Rightarrow x= 6, x = -7 $$ \$$

then two consecutive number   $$x = 6, (x + 1) = 6 +1 = 7 $$\$$

 

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