Question

the difference of square two numbers is 119 . if the larger is 2 more than the twice of the smaller number, then find the two numbers​

Answer 1

Answer:

Step-by-step explanation:

⇒  Let smaller number be x and larger number be y

According to the question,

⇒  y

2

−x

2

=88         ------ ( 1 )

⇒  y=2x−5              ----- ( 2 )

Substituting value of y from equation (2) in ( 1 )$$,

(2x−5)

2

−x

2

=88

⇒  4x

2

−20x+25−x

2

−88=0

⇒  3x

2

−20x−63=0

⇒  3x

2

−27x+7x−63=0

⇒  3x(x−9)+7(x−9)=0

⇒  (x−9)(3x+7)=0

⇒  x−9=0 and 3x+7=0

⇒  x=9 and x=−

3

7

​

Number cannot be negative.

∴  Smaller number =9

⇒  Larger number =2x−5=2×9−5=18−5=13

⇒  Product of two numbers =9×13=117

Answer 2

$\bold{ANSWER≈}$

Step-by-step explanation:

→ Let smaller number be x and larger

number be y

According to the question,

→ y

2

-X

2

#88

y=2x-5

-(1)

Substituting value of y from equation (2)

in (1)$$,

(2x-5)

2

----(2)

2

=88

<-> 4x

2

-20x+25-x

2

-88-0

- 3x

2

-20X-63-0

→3x

2

-27x+7x-63-0

→ 3x(x-9)+7(x-9)=0

- (x-9)(3x+7)=0

→x-9=0 and 3x+7=0

→ x=9 and x=

3 7

Number cannot be negative.

:: Smaller number =9

→ Larger number =2x-5=2×9-5=18-5-13

→ Product of two numbers =9x13-117