Question

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Question:-


Give me all formulas of chapter- 1 (Number system) of class 9th.


Best answer will be mark as brainleist.​

Answer 1

Answer:

1. (α+в)²= α²+2αв+в²

2. (α+в)²= (α-в)²+4αв

3. (α-в)²= α²-2αв+в²

4. (α-в)²= (α+в)²-4αв

5. α² + в²= (α+в)² - 2αв.

6. α² + в²= (α-в)² + 2αв.

7. α²-в² =(α + в)(α - в)

8. 2(α² + в²) = (α+ в)² + (α - в)²

9. 4αв = (α + в)² -(α-в)²

10. αв ={(α+в)/2}²-{(α-в)/2}²

11. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)

12. (α + в)³ = α³ + 3α²в + 3αв² + в³

13. (α + в)³ = α³ + в³ + 3αв(α + в)

14. (α-в)³=α³-3α²в+3αв²-в³

15. α³ + в³ = (α + в) (α² -αв + в²)

16. α³ + в³ = (α+ в)³ -3αв(α+ в)

17. α³ -в³ = (α -в) (α² + αв + в²)

18. α³ -в³ = (α-в)³ + 3αв(α-в)

Answer 2

Answer:

Any number that can be written in the form of p ⁄ q where p and q are integers and q ≠ 0 are rational numbers. Irrational numbers cannot be written in the p ⁄ q form.

There is a unique real number which can be represented on a number line.

If r is one such rational number and s is an irrational number, then (r + s), (r – s), (r × s) and (r ⁄ s) are irrational.

For positive real numbers, the corresponding identities hold together:

\(\sqrt{ab}\) = \(\sqrt{a} × \sqrt{b}\)

\(\sqrt{\tfrac{a}{b}}\) = \(\frac{\sqrt{a}}{\sqrt{b}}\)

\((\sqrt{a}+\sqrt{b})\times(\sqrt{a}-\sqrt{b})=a-b\)

\((a+\sqrt{b})\times(a-\sqrt{b})=a^2-b\)

\((\sqrt{a}+\sqrt{b})^2=a^2+2\sqrt{ab}+b\)

If you want to rationalize the denominator of 1 ⁄ √ (a + b), then we have to multiply it by √(a – b) ⁄ √(a – b), where a and b are both the integers.

Suppose a is a real number (greater than 0) and p and q are the rational numbers.

ap x bq = (ab)p+q

(ap)q = apq

ap / aq = (a)p-q

ap / bp = (ab)p