If √(5x+9)+√(5x-9)=3(2+√2), then √(10x+9) is equal to
Question:
If √(5x+9)+√(5x-9)=3(2+√2), then √(10x+9) is equal to
If √(5x+9)+√(5x-9)=3(2+√2), then √(10x+9) is equal to
Options
Answer: 3√7
Explanation:
Let a=√(5x+9) and b=√(5x-9). Then a+b=3(2+√2) and a^2-b^2=18. From (a+b)^2=9(6+4√2)=54+36√2 and 2ab=(a+b)^2-(a^2+b^2). We get 10x=a^2+b^2=(a+b)^2-2ab. Solving gives √(10x+9)=3√7.
Explanation:
Let a=√(5x+9) and b=√(5x-9). Then a+b=3(2+√2) and a^2-b^2=18. From (a+b)^2=9(6+4√2)=54+36√2 and 2ab=(a+b)^2-(a^2+b^2). We get 10x=a^2+b^2=(a+b)^2-2ab. Solving gives √(10x+9)=3√7.
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