Question
If (x + a) is a common factor of x2 –
(2+√2)x + 2√2 and x2 - 2√2x + 2, then the value of √(5√2 – a)3√2 is :Solution
x2 – (2+√2)x + 2√2 = 0 ------ (i) x2 - 2√2x + 2 = 0 ------ (ii) Now, x + a = 0 => x = -a ------ (iii) Substituting in (i) and (ii), => x2 - (2 + √ 2) x + 2√2 = 0 => a2 - ( 2 + √ 2 ) (-a) + 2√ 2 = 0 => a2 + ( 2 + √ 2 ) a + 2√ 2 = 0 => x2 - 2√ 2 x + 2 = 0 => a2 + 2√ 2 a + 2 = 0 Now, => a2 + ( 2 + √ 2 ) a + 2√ 2 = a2 + 2√ 2 a + 2 2a + √ 2 a + 2√ 2 = 2√ 2 a + 2 2a + √ 2a - 2√ 2 a = 2 - 2√ 2 2a - √ 2a = 2 - 2√ 2 a ( 2 - √ 2 ) = 2 - 2√ 2 a = ( 2 - 2√ 2 ) / ( 2 - √ 2 ) Substituting the value of a in the equation: √ ( 5√ 2 - a ) 3√ 2 = √ ( 5√ 2 - [ ( 2 - 2√ 2 ) / ( 2 - √ 2 ) ] × 3√ 2 = √ [ ( 5√ 2 × ( 2 - √ 2 ) ) - ( 2 - 2√ 2 ) / ( 2 - √ 2 ) ] × 3√ 2 = √ [ ( 10√ 2 - 10 - 2 + 2√ 2 ) / ( 2 - √ 2 ) ] × 3√ 2 = √ [ ( 12√ 2 - 12 ) / ( 2 - √ 2 ) ] × 3√ 2 = √ [ ( (36 × 2) - ( 36 × √ 2 ) ) / ( 2 - √ 2 ) ] = √ ( 72 - 36√ 2) / ( 2 - √ 2 ) = √ 36 ( 2 - √ 2 ) / ( 2 - √ 2 ) = √ 36 = 6 ∴ √ ( 5√ 2 - a ) 3√ 2 = 6
A shopkeeper marked an article Rs. 900 above its cost price and sold it after giving a discount of 20% and earned a profit of 25%. Find the cost price o...
A shopkeeper sold an article after giving a discount of 25% and made a profit of Rs. 40. Find the marked price of the article if cost price of the artic...
Roshan purchased 100 rolls of paper for Rs. 27 per roll. He spent Rs. 600 on their transportation. He also paid 50 paise per roll for packing of each ro...
Two friends Shyam and Ram, Shyam sold an item after allowing two successive discounts of 20% and 15%, While Ram sold the same item after two successive ...
A dealer bought a commodity for Rs. 'w'. He marked it up by Rs. 1,800 over the cost and disposed of it after two successive discounts of 5% and 25%. Wha...
A shopkeeper sold a fridge for Rs. 1200, making a 20% gain. The fridge was marked at Rs. 1400. What was the discount he provided to make only 10% profit?
Aman bought two guitars, ‘P’ and ‘Q’, with cost prices in the ratio 7:9, and sold them at a loss of 10% and a profit of 30%, respectively. If th...
A shopkeeper marks an article 60% above its cost price . During a sale, he gives successive discounts of 20% and 15% . Even after this, he earns...
A dishonest seller, at the time of selling and purchasing uses weight 10% less and 20% more per kg respectively. Find the approx. percent profit earned ...
The ratio between the cost price of product G and H is 8:7 respectively. Each of the products was marked 25% above its cost price. If the MRP of product...
Relevant for Exams:
