10 Dec 2020 2:21 pm

**Tamilnadu, Samacheer, Kalvi, 10th, sslc, Maths, Solutions, Chapter 3, Algebra, Ex 3.6,**.

**Question 1.**

Simplify

(i) \frac{x(x+1)}{x-2}+\frac{x(1-x)}{x-2}**Answer:**

\frac{x(x+1)}{x-2}+\frac{x(1-x)}{x-2} = \frac{x(x+1)+x(1-x)}{x-2}

= \frac{x^{2}+x+x-x^{2}}{x-2}

= \frac { 2x }{ x-2 }

(ii) x+2x+3 + x−1x−2**Answer:**

x+2x+3 + x−1x−2 = (x+2)(x−2)+(x−1)(x+3)(x+3)(x−2)

(iii) x3x−y+y3y−x = x3x−y+y3−1(x−y)

Answer:

= x3x−y−y3x−y

= x3−y3x−y (using a^{3} – b^{3} = (a – b) (a^{2} + ab + b^{2}))

= (x−y)(x2+xy+y2)x−y

= x^{2} + xy + y^{2}

**Question 2.**

Simplify

(i) (2x+1)(x−2)x−4 – (2×2−5x+2)x−4

**Answer:**

(ii) 4xx2−1−x+1x−1**Answer:**

**Question 3.**

Subtract 1×2+2 from 2×3+x2+3(x2+2)2

Answer:

**Question 4**.

Which rational expression should be subtracted from x2+6x+8×3+8

Answer:

**Question 5.**

If A = 2x+12x−1, B = 2x−12x+1 find 1A−B – 2BA2−B2**Answer:**

**Question 6.**

If A = xx+1 B = 1x+1 prove that (A+B)2+(A−B)2A+B=2(x2+1)x(x+1)2**Answer:**

**Question 7.**

Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?**Solution:**

Pari: time required to complete the work = 4 hrs.

∴ In 1 hr. he will complete = 14 of the work.

= 14 w.

Yuvan: Time required to complete the work = 6 hrs.

∴ In 1 hr. he will complete the 16 of the work

= 16 w

Working together, in 1 hr. they will complete w4+w6 of the work.

= 6w+4w24=512w

∴ To complete the total work time taken

= w512w=125 = 2.4 hrs. [∵ (4) hrs = 4 × 60 = 24 min]

= 2 hrs 24 minutes.

**Question 8.**

Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ? 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?

**Solution**

Let the weight of applies be a kg.

Let the weight of bananas be b kg.

a + b = 50

ax = ₹ 1800 ………….. (1)

by = ₹ 600 ………… (2)

x = 2y …………… (3)

Use (3) in (1) ⇒ a(2y) = 1800

y = 900a ………….. (4)

Use (4) in (2) ⇒ b900a = 600

∵ 3b = 2a …………….. (5)

∵ a + b = 50

a + 2a3 = 50 ⇒ 5a3 = 50

⇒ a = 50 × 35

= 30

∴ b = 20

∴ Iniya bought 30 kg of applies and 20 kg of bananas

= 30

.’. b = 20.

.’. Iniya bought 30 kg of applies and 20 kg of bananas.