Question

If 2x-3y=4 , 2x+3y=5 what is the value of 9x*x+4y*y

Answer 1

$9x {}^{2} + 4y {}^{2} =( 3x) {}^{2} + (2y) {}^{2} \\ = (3x + 2y) {}^{2} - 12xy \\ = ( \frac{27}{4} + \frac{1}{3} ) {}^{2} - 2( \frac{27}{4} )( \frac{1}{3} ) \\ = \frac{6577}{144}$

now ...

2x+3y=5

2x-3y=4

therefore...4x=9

=>X=9/4=>3x=27/4

therefore..y=1/6=>2y=1/3

now....

Answer 2

$\bold\pink {\bf {\underline {Given:-}}}$

▪${ \tt{2x - 3y = 4}}$

▪${ \tt{2x + 3y = 4}}$

$\bold\purple {\bf {\underline {To\:Find:-}}}$

▪The value of ${\tt{9 {x}^{2} + 4 {y}^{2}}}$

$\huge\bold\red{\bf {\underline {Solution:-}}}$

After adding the equations, we got,

${ \tt{4x = 9}}$

$⟹ {\tt{x = \frac{9}{4}}}$

✷ $\bold {\bf{Hence,\:The\:Value\:of\:x\:is\:\frac {9}{4}}}$

Now, after putting the value of ${\tt {x}}$ in the 2ⁿᵈ equation we got,

${ \tt{2 \times \frac{9}{4} + 3y = 5}}$

$⟹ { \tt{\frac{9}{2} + 3y = 5}}$

$⟹ { \tt{3y = 5 - \frac{9}{2} }}$

$⟹ {\tt{3y = \frac{10 - 9}{2} }}$

$⟹{ \tt{3y = \frac{1}{2} }}$

$⟹ { \tt{ y= \frac{1}{6} }}$

✷ $\bold{\bf{Hence,\:the\:value\:of\:y\:is\:\frac {1}{6}}}$

_______________________________

After putting the value of ${\tt {x}}$ and ${\tt {y}}$ in the given expression, we got,

${ \tt{9 \times {( \frac{9}{4} )}^{2} + 4 \times { (\frac{1}{6} )}^{2} }}$

$⟹{ \tt{9 \times \frac{81}{16} + 4 \times \frac{1}{36} }}$

$⟹ { \tt{\frac{729}{16} + \frac{4}{36} }}$

$⟹{ \tt{ \frac{729}{16} + \frac{1}{9}}}$

$⟹ {\tt{ \frac{6561 + 16}{144} }}$

$⟹{ \tt{ \frac{6577 }{144} }}$

$\bold\green {\bf {Answer:\frac {6577}{144}}}$