Question

1. Simplify:

(√5x - √2y)(√5x + √2y)

a) (5x - 2y)
b) 5x^2 - 2y^2
c) (5x - 2y)^2
d) 3

2. The angles of the triangle are 3x-40,x+20 and 2x-10 then the value of x is

a) 40°
b) 35°
c) 50°
d) 45°

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Answer 1

Answer:

1)Option b

2)option b

Step-by-step explanation:

1)Given that :(√5x - √2y)(√5x + √2y)

This is in the form of (a+b)(a-b)

Here, a=√5x and b=√2y

we know that (a+b)(a-b) =a²-b²

=>(√5x - √2y)(√5x + √2y)

=>(√5x)²-(√2y)²

=>5x²-2y²

(√5x - √2y)(√5x + √2y)=5x²-2y²

2)Given angles of a triangle are 3x-40,x+20 and 2x-10

we know that The sum of angles in a triangle =180°

=>3x-40+x+20+2x-10=180°

=>6x-30=180°

=>6x=180+30

=>6x=210°

=>x=210°/6

=>x=35°

The value of X=35°

Answer 2

1) Apply Difference of Two Squares Formula : (a - b)(a + b) = a² - b²

(√5x - √2y)(√5x + √2y)

⇒ (√5x)²- (√2y)²

⇒ 5x²- 2y²

2) (3x - 40) + (x + 20) + (2x - 10) = 180°     [Angle Sum Property]

⇒ 3x - 40 + x + 20 + 2x - 10 = 180°

⇒ 3x + x + 2x - 40 + 20 - 10 = 180°

⇒ 6x - 40 + 20 - 10 = 180°

⇒ 6x - 20 - 10 = 180°

⇒ 6x - 30 = 180°

⇒ 6x - 30 + 30 = 180° + 30

⇒ 6x = 210°

⇒ 6x/6 = 210°/6

⇒ x = 35°