Question

If 3x-7y=10,xy=-1, find the value of 9x square minus 49y square

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{9x^2\:-\:49y^2\:=\:40}}\:\:\star}$

Explanation :

Given :–

• 3x - 7y = 10
• xy = (-1)

To Find :–

• 9x² - 49y² = ?

Formula Applied :–

• $\boxed{\star\:\:\bf{(a\:-\:b)^2\:=\:a^2\:-\:2ab\:+\:b^2}\:\:\star}$

• $\boxed{\star\:\:\bf{(a\:+\:b)^2\:=\:a^2\:+\:2ab\:+\:b^2}\:\:\star}$

• $\boxed{\star\:\:\bf{(a\:-\:b)(a\:+\:b)\:=\:a^2\:-\:b^2}\:\:\star}$

Solution :–

We have ,

• 3x - 7y = 10
• xy = (-1)

Putting these values in the Formula :

$\rightarrow\sf{(a\:-\:b)^2\:=\:a^2\:-\:2ab\:+\:b^2}$

$\rightarrow\sf{(3x\:-\:7y)^2\:=\:(3x)^2\:-\:2(3x)(7y)\:+\:(7y)^2}$

$\rightarrow\sf{(10)^2\:=\:9x^2\:-\:42xy\:+\:49y^2}$

$\rightarrow\sf{100\:=\:9x^2\:+\:[(-42)\:\times\:(-1)]\:+\:49y^2}$

$\rightarrow\sf{100\:=\:9x^2\:+\:42\:+\:49y^2}$

$\rightarrow\sf{9x^2\:+\:49y^2\:=\:100\:-\:42}$

$\rightarrow\sf{9x^2\:+\:49y^2\:=\:58}$

Now , we have ,

• 9x² + 49y² = 58
• xy = (-1)

Putting these values in the Formula :

$\rightarrow\sf{(a\:+\:b)^2\:=\:a^2\:+\:2ab\:+\:b^2}$

$\rightarrow\sf{(3x\:+\:7y)^2\:=\:(3x)^2\:+\:2(3x)(7y)\:+\:(7y)^2}$

$\rightarrow\sf{(3x\:+\:7y)^2\:=\:9x^2\:+\:42xy\:+\:49y^2}$

$\rightarrow\sf{(3x\:+\:7y)^2\:=\:(9x^2\:+\:49y^2)\:+\:42(-1)}$

$\rightarrow\sf{(3x\:+\:7y)^2\:=\:58\:-\:42}$

$\rightarrow\sf{(3x\:+\:7y)^2\:=\:16}$

$\rightarrow\sf{3x\:+\:7y\:=\:\sqrt{16}}$

$\rightarrow\bf{3x\:+\:7y\:=\:4}$

We have found that ,

• 3x - 7y = 10
• 3x + 7y = 4

Putting these values in the Formula :

$\rightarrow\sf{(a\:-\:b)(a\:+\:b)\:=\:a^2\:-\:b^2}$

$\rightarrow\sf{(3x\:-\:7y)(3x\:+\:7y\:=\:(3x)^2\:-\:(7y)^2}$

$\rightarrow\sf{(10)(4)\:=\:9x^2\:-\:49y^2}$

$\rightarrow\boxed{\bf{9x^2\:-\:49y^2\:=\:40}}$

∴ The value of 9x² - 49y² will be 40 .

Answer 2

Hi ,

3x - 7y = 10 --- ( 1 )

xy = -1 ---( 2 )

Do the Square of equation ( 1 ) , we

get ,

( 3x - 7y )² = 10²

( 3x )² + ( 7y )² - 2 × 3x × 7y = 100

9x² + 49y² - 42xy = 100

9x² + 49y² - 42 × ( -1 ) = 100

9x² + 49y² + 42 = 100

9x² + 49y² = 100 - 42

= 58

I hope this helps you.

: )