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We offer help in almost all topics in math. A few are mentioned below.

** Free math tutoring topics**

We offer help in almost all topics in math. A few are mentioned below.

- Pre Algebra
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## Free Online Tutoring for Math

Following are few examples of solved problems.

**Example 1: -**

If the letters of the word " FATHER" are arranged alphabetically as in a dictionary, show that it will occur as the 261 word.

**Solution: -**

There are six letters in the word "FATHER". Since the words are arranged alphabetically, first comes the words starting with A. Then starting with E and then comes the words starting with F. To find the number of words beginning with A, keep A fixed at the first letter and arrange the remaining 5 letters. This can be done in 5! = 120 ways. Similarly the number of words starting with E is 120. Therefore the total number of words beginning with A and E is 240. Now the words begin with F. To find the words beginning with FA, arrange the remaining 4 letters which can be done in 4! = 24 ways. The 241th word is" FAEHRT" and 240+24 = 264 th word is "FATRHE". THE 263RD WORD IS :fatreh" and the 262nd word is "FATHRE".

**Therefore, the 261th word is "FATHER".**

**Example 2: -**

If the roots of the equation x

^{2}- 2x + 7 = 0 are α and β, find the equation whose roots are α

^{2}+ β and β

^{2}+ α

**Solution: -**

Since α and β are the roots of the equation x

^{2}- 2x + 7 = 0, α + β = 2 and αβ = 7.

Now sum of the roots α

^{2}+ β + β

^{2}+ α = α

^{2}+ β

^{2}+ α + β

=(α + β)

^{2}- 2αβ + α + β

= 2

^{2}- 2 x 7+ 2

= 4 -14 + 2 = -8

Product of the roots = (α

^{2}+ β)( β

^{2}+ α) = α

^{2}β

^{2}+ α

^{3}+ β

^{3}+ αβ

= α

^{2}β

^{2 }+ (α + β)

^{3}- 3αβ(α + β) + αβ

= 7

^{2}+ 2

^{3}- 3 x 7 x 2 + 7

= 49 + 8 - 42 + 7

= 22

Therefore the equation whose roots are α

^{2}+ β and β

^{2}+ α is

x

^{2}- (sum of the roots)x + product of the roots = 0

That is

**x**

Example 3: -

The sum of three numbers in Arithmetic Progression is 42 and their product is 2618. Find the numbers.

^{2}+ 8x + 22 = 0Example 3: -

**Solution: -**

Let the numbers be a - d, a, a + d

Given that the sum of the number is 42.

That is a - d + a + a + d = 42

3a = 42

That is a = 42/3 =14.

Also given product of the numbers is 2618

That is (a - d) a(a + d) = 2618

a(a

^{2}- d

^{2}) = 2618

14(14

^{2}-d

^{2}) = 2618

Dividing both sides by 14, we get

14

^{2}-d

^{2}= 187

subtracting 142 from both sides, we get

-d

^{2}= -9

That is d = ± 3

**When d = 3 and a = 14, the numbers are 11, 14, 17.**

When d = -3 and a = 14, the numbers are 17, 14, 11.

When d = -3 and a = 14, the numbers are 17, 14, 11.