Maths Equations ||Part 1|| Shashaank Blogspot

MATH

EQUATIONS

1.  If (3x+4)2 +(3x-2)2=(6x+5)(3x-2)+12 then find the value of x

1. 2

2. 1

3. -3

4.-2

Solution:-

(D)

(3x+4)2 +(3x-2)2=(6x+5)(3x-2) + 12 

→  9x2 + 24x+16 + 9x2 + 12x + 4 = 18x2 + 3x - 10 + 12 

→ 18x2 + 12x +20 = 18x2 +3x + 2 

→ 9x + 18 

→ x = -2

NOTE :- 

→ You guys can see 9x2,18x2 

→ It Means 9 to the power of 2 

2. The sum of numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator it becomes 2 by 3. Find the fraction​.

Solutions :-

→ Let the numerator = x

→ denominator = y

According to question,

→ x + 1 / y + 1 = 2 / 3

→ 3x + 3 = 2y + 2

→ 3x - 2y = -1 ----------------1

→ x - 1 / y - 1 = 3 / 5

→ 5x - 5 = 3y - 3

→ 5x - 3y =2 ------------------2

We get 2 question , Now by Elimination Method ,

→ 3x - 2y = -1 × 5

→ 5x - 3y = 2 × 3

→ 15x - 10y = -5

→ 15x - 9y = 6 

→ -y = -11

→ y = 11

Now put the value of in equation 1

→ 3x - 2(11) = - 1

→ 3x - 22 = -1

→ 3x = 21

→ x = 7

→ So that the value of x is and y is 11.

→ We know numerator = x and denominator = y

→ Numerator / Denominator = 7 / 11

→ So that the fraction is 7 / 1

3. If  (x+1/x+2 )2 = x+2/x+4  then x = ?

Solutions : -

4.The length of a rectangle is 3 times its breadth, if the length is decreased by 3 cm and the breadth increased by 5 cm the area of the rectangle is increased by 57cm2. Find the perimeter of rectangle.

Solution:-

Correct option is

B

48 cm

Let the breadth of the rectangle be x cm.
Then, length = 3x cm

New breadth =(x+5) cm
New length =(3x−3)cm

Then, (x+5)(3x−3)−3x×x=57
⇒3x2+12x−15−3x2=57
⇒12x=57+15=72⇒x=6
∴ Breadth  = 6 cm, Length = 18 cm
Perimeter =2(6cm+18cm)=2×24cm=48 cm

5. Two irrational numbers between 2 and 3

Solution:-

Answer:

→ 

→ 

is the irrational no between 2 and 3

6. 

Correct option is C

2.2

The given equation is

x2−7x+12x2−5x+6​=x2+7x+10x2−x−6​

⟹(x−3)(x−4)(x−3)(x−2)​=(x+5)(x+2)(x−3)(x+2)

​⟹x−4x−2​=x+5x−3​

⟹x2+3x+10=x2−7x+12

⟹10x=22

⟹x=2.2.

HOPE IT HEPLS

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2The perimeter  of the rectangle is