Write each of the following numbers as difference of the square of two consecutive natural numbers. (i) 49 (ii) 75 (iii) 125
Answers
Answer:
i)24 and 25 ii)37 and 38 iii)62 and 63
Step-by-step explanation:
Let one Natural number be x
Another natural number=x+1
i)Difference of their squares=49
(x+1)²-x²=49
x²+2x+1-x²=49
2x=48
x=24
Two consecutive Numbers are 24 and 25.
ii)Difference of their squares =75
(x+1)²-x²=75
x²+2x+1-x²=75
2x=74
x=37
The consecutive numbers are 37 and 38
iii)Difference of their squares =125
(x+1)²-x²=125
x²+2x+1-x²=125
2x=124
x=62
The consecutive numbers are 62 and 63
Answer:
i)24 and 25 ii)37 and 38 iii)62 and 63
Step-by-step explanation:
Let one Natural number be x
Another natural number=x+1
i)Difference of their squares=49
(x+1)²-x²=49
x²+2x+1-x²=49
2x=48
x=24
Two consecutive Numbers are 24 and 25.
ii)Difference of their squares =75
(x+1)²-x²=75
x²+2x+1-x²=75
2x=74
x=37
The consecutive numbers are 37 and 38
iii)Difference of their squares =125
(x+1)²-x²=125
x²+2x+1-x²=125
2x=124
x=62
The consecutive numbers are 62 and 63