Question

((√7+√5)^2)+((√7-√5)^2)


solve this by step by step​

Answer 1

Answer:

(√7 +√ 5 ) ^2= 7+5 (√7-√5) ^2=7-5

(7+5) +(7-5)

(a+b) (a-b) =a^2+b^2

7^2 - 5^2 =49-25= 24

Answer 2

Answer:

24

Step-by-step explanation:

$( \sqrt{7} + \sqrt{5} )^{2} = ({ \sqrt{7} })^{2} + ( { \sqrt{5} })^{2} + 2 \times \sqrt{7} \times \sqrt{5}$

$= 7 + 5 + 2 \sqrt{35}$

and

$( \sqrt{7} - \sqrt{5} ) ^{2} = ( { \sqrt{7} })^{2} + ( { \sqrt{5} })^{2} - 2 \times \sqrt{7} \times \sqrt{5}$

$= 7 + 5 - 2 \sqrt{35}$

So,

$12 + 2 \sqrt{35} + 12 - 2\sqrt{35}$

$= 24$

#InShort

Remember:

$(x + y)^{2} + (x - y)^{2} = 2( {x}^{2} + {y}^{2} )$

Here,

$x = \sqrt{7} \\ y = \sqrt{5}$

So,

=$2(( { \sqrt{7} })^{2} + ({ \sqrt{5} })^{2} ))$

=$2(7 + 5)$

=$2 \times 12$

=$24$