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Yogita Ingle 4 years, 5 months ago
Let us assume √2 is rational number.
a rational number can be written into he form of p/q
√2=p/q
p=√2q
Squaring on both sides
p²=2q²__________(1)
.·.2 divides p² then 2 also divides p
.·.p is an even number
Let p=2a (definition of even number,'a' is positive integer)
Put p=2a in eq (1)
p²=2q²
(2a)²=2q²
4a²=2q²
q²=2a²
.·.2 divides q² then 2 also divides q
Both p and q have 2 as common factor.
But this contradicts the fact that p and q are co primes or integers.
Our supposition is false
.·.√2 is an irrational number.
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Rajan Kumar Pasi 4 years, 5 months ago
Present | Future ( +10 years ) | Relation |
Father (x) | x + 10 | double of sons age |
Son (y) | y + 10 | age |
Therefore, x + 10 = 2 (y + 10)
=> x + 10 = 2y + 20
=> x - 2y = 10.
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Yogita Ingle 4 years, 5 months ago
x+y=12 ------(1)
Squaring equation 1 on both sides
(x+y)² = 12²-----(2)
(a+b)²=a²+2ab+b²
Now comparing (x+y)² with (a+b)² here a=x and b=y
So Equation 2 becomes
(x+y)² = 12²
x²+2xy+y² =12²
x²+y² = 144 - 2xy----(3)
But in question its given that xy= 32
So, substituting xy = 32 in equation 3
x²+y² =144-2*32
x²+y² =144-64 = 80.
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Sylvia Sylvia 4 years, 5 months ago
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