Question

If 5,7=37
8&4=20
10 & 6=34
Then 6 &4= ?

Answer 1

Given

If 5,7=37

8&4=20

10 & 6=34

To find

6 &4= ?

Solution :

5,7=37

The 5,7 can be written as

$5^{2} \ + 7^{2} \\=\ 25 +49\\=74\\7-5=\ 2\\\frac{74}{2}\\ =37$

The 8&& 4 can be written as

$8&4\\=8^{2}\ +4^{2} \\ =80\\8-4=4\\\frac{80}{4}\\ =20$

10 & 6 can be written as

$10^{2}\ +6^{2}\\ =\ 100+36\\=136\\10-6=4\\\frac{136}{4}\\ =34$

Therefore 6 &4 can be written as

$6^{2}\ + \ 4^{2}\\ =36+16\\\=52\\6-4=2\\\frac{52}{2}\\ =26$

Answer 2

Given data :

Sets are

5 7 (37)   ;   8 4 (20)   ;   10 6 (34)

To find :  

The missing number in 6 4 (?)  

Solution:

Logic applied behind :

Let A, B, C are the three numbers in the given set respectively.

Then, apply C = ( A² - B²) / | A - B |

5 7 (37), Here C = 37 :

A = 5, B = 7

Then, ( 5² + 7² ) / | 5 - 7 |

       = (25 + 49) / |-2|

       = 74/2

       = 37         [=C]

8 4 (20), Here C = 20 :

A = 8, B = 4

Then, ( 8² + 4² ) / | 8 - 4 |

       = (64 + 16) / |4|

       = 80/4

       = 20         [=C]

10 6 (34), Here C = 34 :

A = 10, B = 6

Then, ( 10² + 6² ) / | 10 - 6 |

       = (100 + 36) / |4|

       = 136/4

       = 34         [=C]

6 4 (?), Here C = ? :

A = 6, B = 4

So, C = ( 6² + 4² ) / | 6 - 4 |

        = (36 + 16) / |2|

        = 52/2

        = 26         [=C]

So, 26 is the answer.

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