: 1. सूरज से हम और क्या-क्या सीख सकते हैं? 2. कवितानुसार लता और पेड़ों से हमें क्या सीखना चाहिए?
Answers
Explanation:
Answer :–
The first number = 13.
The second number = 26.
The third number = 39.
Given :–
Three numbers are in the ratio = 1 : 2 : 3.
The sum of their cubes = 79092.
To Find :–
Find all the three numbers.
Solution :–
Let,
The first number be 1x.
The second number be 2x.
The third number be 3x.
According to the question,
The sum of their cubes is 79092.
Thay means,
\rightarrow {(x)}^{3} + {(2x)}^{3} + {(3x)}^{3} = 79092→(x)
3
+(2x)
3
+(3x)
3
=79092
Now, open the brackets.
\rightarrow {x}^{3} + {8x}^{3} + {27x}^{3} = 79092→x
3
+8x
3
+27x
3
=79092
\rightarrow{36x}^{3} = 79092→36x
3
=79092
\rightarrow {x}^{3} = \cancel\dfrac{79092}{36}→x
3
=
36
79092
\rightarrow{x}^{3} = \cancel \dfrac{39546}{18}→x
3
=
18
39546
\rightarrow {x}^{3} = \cancel \dfrac{19773}{9}→x
3
=
9
19773
\rightarrow {x}^{3} = \cancel\dfrac{6591}{3}→x
3
=
3
6591
\rightarrow {x}^{3} = 2197→x
3
=2197
\rightarrow x = \sqrt[3]{2197}→x=
3
2197
\rightarrow x = 13→x=13
So,
we get the value of x is 13.
Now, we have to find the numbers.
So,
The first number = 1x = 1 × 13 = 13.
The second number = 2x = 2 × 13 = 26.
The third number = 3x = 3 × 13 = 39.
Hence,
The three numbers are 13, 36 and 39.
Verification :–
According to the question,
The sum of their cubes is 79092.
We have,
First number = 13.
Second number = 26.
Third number = 39.
Now, substitute the values of all the three numbers.
\rightarrow {(13)}^{3} + {(26)}^{3} + {(39)}^{3} = 79092→(13)
3
+(26)
3
+(39)
3
=79092
\rightarrow 2197 + 17576+ 59319 = 79092→2197+17576+59319=79092
\rightarrow 79092 = 79092→79092=79092
Hence Verified !!
Answer:
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