find the square of 42 without using identity
Answers
Answer:
Given:
Two numbers are in the ratio of 2 : 3.
If 15 is added to both the numbers the ratio becomes ¹¹⁄14.
To find:
The Greatest number?
Solution: Let consider the smaller number be 2m and Greater number be 3m.
★ Adding 15 to both numbers,
Smaller number = (2m + 15)
Greater number = (3m + 15)
• According to Question,
After adding 15 to both the numbers the ratio b/w two numbers becomes ¹¹⁄14.
➟ (2m + 15)/(3m + 15) = ¹¹⁄14
➟ 14(2m + 15) = 11(3m + 15)
➟ 28m + 210 = 33m + 165
➟ 28m – 33m = 165 – 210
➟ – 5m = – 45
➟ m = 45⁄5⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ [∵ –ve sign cancelled]
➟ m = 9
Therefore,
Smaller number, 2m = 2(9) = 18
Greater number, 3m = 3(9) = 27
∴ Hence, the Greater number is 27.
\rule{230px}{.2ex}
• V E R I F I C A T I O N :
After adding 15 to both the numbers the ratio b/w two numbers becomes ¹¹⁄14. So, Let's Verify the answer by Substituting the value of m —
⇥ (2m + 15)/(3m + 15) = ¹¹⁄14
⇥ (2(9) + 15)/(3(9) + 15) = ¹¹⁄14
⇥ (18 + 15)/(7 + 15) = ¹¹⁄14
⇥ 33⁄42 = ¹¹⁄14
⇥ ¹¹⁄14 = ¹¹⁄14 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ∴ Hence Verified!