Question

26. Solve this question
Please give verified answer with step by step solution​

Answer 1

Answer: 10

Assume :

a = 1.5

b = 4.7

c = 3.8

It is in the form of:

(a³+b³+c³ - 3abc) / (a² + b² + c² - ab - bc - ac)

= [(a + b+ c)(a² + b² + c² -ab - bc - ac)] / (a² + b² + c² - ab - bc - ac)

= a + b + c

= 1.5 + 4.7 + 3.8

= 10

Thus, answer is 10.

Answer 2

10

Step-by-step explanation:

To find:

The value of,

$\dfrac{ {(1.5)}^{3} + {(3.8)}^{3} + {(4.8)}^{3} - 3 \times 1.5 \times 4.7 \times 3.5}{ {(1.5)}^{2} + (4.7) {}^{2} + {(3.8)}^{2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 1.5 \times 3.8 }$

Solution:

We can solve it by using Formula,

a³ + b³ + c³ - 3abc

= (a+b+c)(a² +b² +c²-ab-bc-ac)

Let, a = 1.5, b = 3.8 and c = 4.8

Now,

$= \dfrac{ {(1.5)}^{3} + {(3.8)}^{3} + {(4.7)}^{3} - 3 \times 1.5 \times 4.7 \times 3.5}{ {(1.5)}^{2} + (4.7) {}^{2} + {(3.8)}^{2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 1.5 \times 3.8 } \\ \\ = \dfrac{ {(a)}^{3} + {(b)}^{3} + {(c)}^{3} - 3 \times a \times b \times c}{ {(a)}^{2} + (b) {}^{2} + {(c)}^{2} - a \times b - b \times c - a \times c } \\ \\ = \frac{(a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)}{( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)} \\ \\ = \frac{(a + b + c) \cancel{( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)}}{\cancel{( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)}} \\ \\ = (a + b + c) \\ \\ = 1.5 + 4.7 + 3.8 \\ \\ = 10.0 \\ \\ = 10$

Therefore, the required answer is 10.