Question

Maths Number system..
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Brilliant will be given....
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Answer 1

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✤ Required Answer:

✒ GiveN:

• There are 3 questions related to number system and algebraic identities.

✒ To FinD:

• Their respective answers !$!$

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✤ How to solve?

For solving the above question, just be clear that you know the basic identities of algebra such as:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³

☀️ Other than this, we will just modify these formulas to get newer ones and find the solutions of the questions.

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✤ Solution:

8) Given,

➝ x + 1/x = 5

Squaring both sides,

➝ x² + 2 × x × 1/x + 1/x² = 25

➝ x² + 2 + 1/x² = 25

➝ x² + 1/x² = 23

• ANSWER - 23 (C)

9) We know,

➝ (a + b)³ = a³ + 3ab(a + b) + b³

Then,

➝ a³ + b³ = (a + b)³ - 3ab(a + b)

➝ a³ + b³ = (a + b)[(a + b)² - 3ab]

➝ a³ + b³ = (a + b)[a² + 2ab + b² - 3ab]

➝ a³ + b³ = (a + b)(a² - ab + b²)

• ANSWER - (a + b)(a² - ab + b²) (A)

10) Given Number,

➝ 2³ × 3⁴ × 5⁴ × 7

Combining the required terms,

➝ 2³ × 3⁴ × 5³ × 5 × 7

➝ (2 × 5)³ × 3⁴ × 5 × 7

➝ 10³ × 3⁴ × 5 × 7

➝ 2835 × 10³

So, at the last there would be 3 zeroes.

We can predict this by,

We know that 10 = 2 × 5

So, comparing powers of 2 and 5 and combining them in order to get the powers of 10 will also result in the ans 3.

• ANSWER - 3 (A)

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Answer 2

Answer:

Hey dude, answer me. Why are we fighting for no reason?