Question

solve for brainleist answer
with method​

Answer 1

Answer:

16

Step-by-step explanation:

Answer 2

Given :-

( a - b ) = 7 and ab = 51.75

To Find :-

$\quad \maltese { \sf { \cfrac{(a² - b²)}{(a - b )} } }$

Solution :-

We knows a algebraic identity ;

$\quad \qquad { \bigstar { \underline { \boxed { \boxed { \sf { \bf { \mathfrak { \pink { a² - b² = ( a + b ) ( a - b ) } } } } } } } { \bigstar } } }$

Now let's start which we have to find ;

$\quad \qquad \maltese { \sf { \cfrac{(a² - b²)}{(a - b )} } }$

${ : \longmapsto { \sf { \cfrac{(a - b) (a + b)}{(a - b )} \quad \qquad { \bigg [ \because a² - b² = ( a + b ) ( a - b ) } \bigg ] } } }$

After Cancelling ( a - b ) we gets ;

${ : \longmapsto { \sf { ( a + b ) } } }$

We also knows another identity ;

$\quad \qquad { \bigstar { \underline { \boxed { \boxed { \sf { \bf { \mathfrak { \pink { ( a - b )² = a² + b² - 2ab } } } } } } } { \bigstar } } }$

Putting all the known values we have ;

${ : \longmapsto { \sf { ( 7 )² = a² + b² - 2 × 51.75 } } }$

${ : \longmapsto { \sf { 49 = a² + b² - 103.50 } } }$

${ : \longmapsto { \sf { a² + b² = 49 + 103.5 } } }$

$: \longmapsto { \sf { a² + b² = 152.5 } }$

Adding " 2ab " to both sides we get ;

${ : \longmapsto { \sf { a² + b² + 2ab = 152.5 + 2ab } } }$

Put the value of " ab " on RHS ;

${ : \longmapsto { \sf { a² + b² + 2ab = 152.5 + 2 × 51.75 } } }$

${ : \longmapsto { \sf { a² + b² + 2ab = 152.5 + 103.5 } } }$

${ : \longmapsto { \sf { a² + b² + 2ab = 256 } } }$

We knows another Identity i.e ;

$\quad \qquad { \bigstar { \underline { \boxed { \boxed { \sf { \bf {\mathfrak {\pink { ( a + b )² = a² + b² + 2ab } } } } } } } { \bigstar } } }$

So By using this identity we have ;

${ : \longmapsto { \sf { ( a + b )²= 256 } } }$

${ : \longmapsto { \sf { ( a + b ) = \sqrt{256} } } }$

${ : \longmapsto { \sf { ( a + b ) = \pm 16 } } }$

But as here only Positive values are given . So , our Answer is 16

Henceforth , The Required Answer is Option ( 1 ) 16 !