Question

the sum of the squares of two consecutive numbers is 365. find the numbers.

Answer 1

Answer:

13 , 14

Step-by-step explanation:

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Answer 2

Answer:

13 and 14

Step-by-step explanation:

Let the two consecutive numbers be x and (x+1)

Then,

x²+(x+1)²=365

x²+x²+2x+1=365

2x²+2x+1-365=0

2x²+2x-364=0

2(x²+x-182)=0

x²+x-182=0

By using Quadratic equation;

x= {-b±√√b²-4ac}/2a

here; b=1 ,a=1 & c= –182

so,x= {-1±√1-4×1×(-182)}/2×1

= (-1±√1+728)/2

= -1±27/2

x= (-1+27)/2 or x= (-1-27)/2

x=13 or x= -14 (not negative)

so, x=14

(ans)