Question

if a equal to square root 2 + 1 by square root 2 - 1 and b equal to square root 2 minus 1 by square root 2 + 1 then find the value of a square minus b square minus 4 a b

Answer 1

Answer:

The square root of 2, or the one-half power of 2, written in mathematics as {\displaystyle {\sqrt {2}}}{\sqrt {2}} or {\displaystyle 2^{1/2}}2^{{1/2}}, is the positive algebraic number that, when multiplied by itself, equals the number 2.[1] Technically, it must be called the principal square root of 2, to distinguish it from the negative number with the same property.

The square root of 2 is equal to the length of the hypotenuse of an isosceles right triangle with legs of length 1.

Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length;[2] this follows from the Pythagorean theorem. It was probably the first number known to be irrational.[3] The fraction

99

/

70

(≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator.

Sequence A002193 in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places:[4]

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