Express the following as the sum of two consecutive numbers. i) 21² ii) 13² iii) 11² iv)19²
Answers
Answer:
Answer
In all the cases ,
let one integer be x
since the integers are consecutive,
other integer = x + 1
Now,
a) (x) + (x + 1) = 21²
2x + 1 = 441
2x = 440
x = 440/2 = 220. and x+1 = 221
So,
the integers are 220 and 221
b) 13²
x + x + 1 = 13²
2x + 1 = 169
2x = 168
x = 168/2 = 84. and x + 1 = 85
So ,
the consecutive integers are 84 and 85
c) 11²
x + x + 1 = 11²
2x + 1 = 121
2x = 120
x = 120/2
x = 60. and x + 1 = 61
So,
the consecutive integers are 60 and 61
d) 19²
x + x + 1 = 19²
2x + 1 = 361
2x = 360
x = 360/2
x = 180. and x + 1 = 181
So,
the consecutive integers are 180 and 181
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Answer:
21²=220+221
13²=84+85
11²=60+61
19²=180+181
Step-by-step explanation:
Given:-
i) 21² ii) 13² iii) 11² iv)19²
To find:-
Express the following as the sum of two consecutive numbers. i) 21² ii) 13² iii) 11² iv)19²
Solution:-
i) Given number=21²=21×21=441
Let the two consecutive numbers be X,X+1
Their sum=X+X+1=2X+1
=>2X+1=441
=>2X=441-1
=>2X=440
=>X=440/2
=>X=220
Now X+1=220+1=221
21²=441=220+221
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ii)Given number=13²=169
Let the two consecutive numbers be X,X+1
=>X+X+1=169
=>2X+1=169
=>2X=169-1
=>2X=168
=>X=168/2
=>X=84
X+1=84+1=85
13²=169=84+85
___________________________________
iii)Given number=11²=121
Let the two consecutive numbers be X,X+1
=>X+X+1=12
=>2X+1=121
=>2X=121-1
=>2X=120
=>X=120/2
=>X=60
X+1=60+1=61
11²=121=60+61
____________________________________
iv)Given number=19²=361
Let the two consecutive numbers be X,X+1
=>X+X+1=361
=>2X+1=361
=>2X=361-1
=>2X=360
=>X=360/2
=>X=180
X+1=180+1=181